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| author | priyanka | 2015-06-24 15:03:17 +0530 |
|---|---|---|
| committer | priyanka | 2015-06-24 15:03:17 +0530 |
| commit | b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b (patch) | |
| tree | ab291cffc65280e58ac82470ba63fbcca7805165 /2915 | |
| download | Scilab-TBC-Uploads-b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b.tar.gz Scilab-TBC-Uploads-b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b.tar.bz2 Scilab-TBC-Uploads-b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b.zip | |
initial commit / add all books
Diffstat (limited to '2915')
157 files changed, 1699 insertions, 0 deletions
diff --git a/2915/CH1/EX1.1/1_1.JPG b/2915/CH1/EX1.1/1_1.JPG Binary files differnew file mode 100755 index 000000000..4e93f7eeb --- /dev/null +++ b/2915/CH1/EX1.1/1_1.JPG diff --git a/2915/CH1/EX1.1/Ex1_1.sce b/2915/CH1/EX1.1/Ex1_1.sce new file mode 100755 index 000000000..15a341e98 --- /dev/null +++ b/2915/CH1/EX1.1/Ex1_1.sce @@ -0,0 +1,24 @@ +clc,clear
+//example 1.1
+//To determine unknown angle in 3 given triangles
+
+//Triangle ABC
+A = 35//angle at vertex A in degrees
+C = 20//angle at vertex C in degrees
+B=180- (A+C) //unknown angle
+printf('Triangle ABC: B = %.0f degree\n',B)
+
+//Triangle DEF
+E = 53//angle at vertex E in degree
+//F = 90, DEF is right triangle
+//So angles E and D are complimentary
+D = 90- E //unknown angle
+printf(' Triangle DEF: D = %.0f degree\n',D)
+
+//Triangle XYZ
+sum_multiple= 1+3+1 //for solvong for alpha
+alpha = 180/ sum_multiple
+X= alpha //unknown angle
+Y= 3* alpha //unknown angle
+Z= alpha //unknown angle
+printf(' Triangle XYZ: X=%.0f degree Y=%.0f degree Z=%.0f degree',X,Y,Z)
diff --git a/2915/CH1/EX1.10/1_10.JPG b/2915/CH1/EX1.10/1_10.JPG Binary files differnew file mode 100755 index 000000000..175aad4f6 --- /dev/null +++ b/2915/CH1/EX1.10/1_10.JPG diff --git a/2915/CH1/EX1.10/Ex1_10.sce b/2915/CH1/EX1.10/Ex1_10.sce new file mode 100755 index 000000000..c74b2ebf1 --- /dev/null +++ b/2915/CH1/EX1.10/Ex1_10.sce @@ -0,0 +1,42 @@ +clc,clear
+//example 1.10
+//To find sine,cosine and tangent functions for 75 degree
+
+//triangle_ADB, angle_BAD = 30
+AB=sqrt(3);BD=1;
+AD=sqrt(AB^2+BD^2); //pythagoras theorem
+
+//angle_DAB + angle_CAB = 75
+//triangle_ABC, angle_BAC = 45
+//pythagoras theorem and 45 degrees
+AC=AB/sqrt(2);BC=AC;
+
+angle_BAC = 45 ; angle_DAB = 30 ;
+angle_DAE = angle_BAC + angle_DAB ;//required angle
+angle_ADE = 90 - angle_DAE ;//complement of DAE
+angle_ADB = 90 - angle_DAB ;//complement of DAB
+
+//Draw BF perpendicular to DE
+angle_BDF = angle_ADB - angle_ADE;
+angle_DBF = 90 - angle_BDF; //complement of BDF
+//By pythagoras theorem and 45 degree
+DF=sqrt(BD/2);FB=DF;
+
+EC=FB;//parallel sides of rectangle
+FE= BC; //parallel sides of rectangle
+DE=DF+FE;//from the figure
+AE=AC-EC;//from the figure
+
+sin_DAE = DE/AD;
+cos_DAE = AE/AD;
+tan_DAE = DE/AE;
+csc_DAE = AD/DE;
+sec_DAE = AD/AE;
+cot_DAE = AE/DE;
+
+printf('sin(%d)=%f\n',angle_DAE,sin_DAE);
+printf('cos(%d)=%f\n',angle_DAE,cos_DAE);
+printf('tan(%d)=%f\n',angle_DAE,tan_DAE);
+printf('csc(%d)=%f\n',angle_DAE,csc_DAE);
+printf('sec(%d)=%f\n',angle_DAE,sec_DAE);
+printf('cot(%d)=%f\n',angle_DAE,cot_DAE);
diff --git a/2915/CH1/EX1.11/1_11.JPG b/2915/CH1/EX1.11/1_11.JPG Binary files differnew file mode 100755 index 000000000..32cd9a09c --- /dev/null +++ b/2915/CH1/EX1.11/1_11.JPG diff --git a/2915/CH1/EX1.11/Ex1_11.sce b/2915/CH1/EX1.11/Ex1_11.sce new file mode 100755 index 000000000..4206af1db --- /dev/null +++ b/2915/CH1/EX1.11/Ex1_11.sce @@ -0,0 +1,11 @@ +clc,clear
+//example 1.11
+//To find the height of the flagpole
+
+//conside the attached figure
+d=150 //distance of person from flagpole in feet
+angle_ele = 32 //angle of elevation in degree
+height_eyes =6 //height of man's eyes
+h= d*tand(angle_ele)
+height_flagpole = height_eyes + h
+printf('Required height of flagpole = %.0f ft',height_flagpole)
diff --git a/2915/CH1/EX1.12/1_12.JPG b/2915/CH1/EX1.12/1_12.JPG Binary files differnew file mode 100755 index 000000000..add9b6b81 --- /dev/null +++ b/2915/CH1/EX1.12/1_12.JPG diff --git a/2915/CH1/EX1.12/Ex1_12.sce b/2915/CH1/EX1.12/Ex1_12.sce new file mode 100755 index 000000000..8a992f79d --- /dev/null +++ b/2915/CH1/EX1.12/Ex1_12.sce @@ -0,0 +1,21 @@ +clc,clear
+//Example 1.12
+//To find the height of mountain
+
+//from the figure
+//h is height of mountain in degree
+//x is distance from base of mountain to the point under top of mountain
+
+d1=400 //initial ditance from base of mountain in feet
+d2=500 //final ditance from base of mountain in feet
+theta1=25 //initial angle of elevation in degrees
+theta2=20 //final angle of elevation in degrees
+
+//from the figure
+//h= (x+d1) * tand(theta1)
+//h= (x+d2) * tand(theta2)
+//eliminating h and solving for x
+x=((d1+d2)*tand(theta2) - d1*tand(theta1))/(tand(theta1)-tand(theta2))
+//substituting x in expression for h
+h= (x+d1) *tand(theta1)
+printf('Height of mountain = %.0f feet',h)
diff --git a/2915/CH1/EX1.13/1_13.JPG b/2915/CH1/EX1.13/1_13.JPG Binary files differnew file mode 100755 index 000000000..81d10036f --- /dev/null +++ b/2915/CH1/EX1.13/1_13.JPG diff --git a/2915/CH1/EX1.13/Ex1_13.sce b/2915/CH1/EX1.13/Ex1_13.sce new file mode 100755 index 000000000..2990126e6 --- /dev/null +++ b/2915/CH1/EX1.13/Ex1_13.sce @@ -0,0 +1,11 @@ +clc,clear
+//Example 1.13
+//To find the horizontal distance from blimp to house
+
+//consider the figure attached
+angle_dep = 24 //angle of depression in degrees
+theta = angle_dep //angle of elevation
+height_blimp = 4280 //height of blimp from ground in feet
+x = height_blimp / tand(theta) //required distance in feet
+
+printf('The house is %.0f ft far from blimp along the ground',x)
diff --git a/2915/CH1/EX1.14/1_14.JPG b/2915/CH1/EX1.14/1_14.JPG Binary files differnew file mode 100755 index 000000000..7f917808f --- /dev/null +++ b/2915/CH1/EX1.14/1_14.JPG diff --git a/2915/CH1/EX1.14/Ex1_14.sce b/2915/CH1/EX1.14/Ex1_14.sce new file mode 100755 index 000000000..c4b8b651e --- /dev/null +++ b/2915/CH1/EX1.14/Ex1_14.sce @@ -0,0 +1,21 @@ +clc,clear
+//Example 1.14
+//To estimate radius of earth when angle of depression is known
+
+angle_dep = 2.23 //angle of depression in degrees
+//In the figure,
+//r is the radius of earth
+//A represent the top of the mountain
+//H be the ocean horizon in the line of sight from A
+//O be the center of the earth
+//B is a point on the horizontal line of sight from A
+
+angle_OAH = 90 - angle_dep ;
+theta = 180 - 90 - angle_OAH ;
+height=3 //height of mountain
+//r is radius of earth to be determined
+
+//distance from top of mountain from centre = r + height
+// cosd(theta)= r/r+height...solving further
+r = height*cosd(theta)/(1-cosd(theta)) ;
+printf('Radius of earth as calculated = %.1f miles\n',r)
diff --git a/2915/CH1/EX1.15/1_15.JPG b/2915/CH1/EX1.15/1_15.JPG Binary files differnew file mode 100755 index 000000000..90c2a61ce --- /dev/null +++ b/2915/CH1/EX1.15/1_15.JPG diff --git a/2915/CH1/EX1.15/Ex1_15.sce b/2915/CH1/EX1.15/Ex1_15.sce new file mode 100755 index 000000000..cceac5493 --- /dev/null +++ b/2915/CH1/EX1.15/Ex1_15.sce @@ -0,0 +1,10 @@ +clc,clear
+//Example 1.15
+// To find the distance from centre of earth to sun
+
+alpha = 0.00244; // equitorial paralalx in degree
+OA = 3956.6; //radius of earth
+angle_OAB = 90;
+
+OB = OA / sind(alpha) ;
+printf('Distance is obtained as %.0f miles = %.0f million miles',OB,OB/10^6)
diff --git a/2915/CH1/EX1.16/1_16.JPG b/2915/CH1/EX1.16/1_16.JPG Binary files differnew file mode 100755 index 000000000..5de22c530 --- /dev/null +++ b/2915/CH1/EX1.16/1_16.JPG diff --git a/2915/CH1/EX1.16/Ex1_16.sce b/2915/CH1/EX1.16/Ex1_16.sce new file mode 100755 index 000000000..3c32b09ea --- /dev/null +++ b/2915/CH1/EX1.16/Ex1_16.sce @@ -0,0 +1,30 @@ +clc,clear
+//Example 1.16
+// To determine the radius of sun
+
+angle_AEB =0 +(32/60)+ (4/60)/60//converting to degrees
+
+//Triangle BES and AES are similar
+//BS=AS as they are radius
+//ES is common to both triangles
+//angle_EBS=angle_ABS =90 as tangents are perpendicualar to radius
+// angle_AES = angle_BES
+angle_AES= angle_AEB /2;
+angle_BES= angle_AEB /2;
+
+//to find ditance from sun to centre of earth
+//obtained from previous example
+alpha = 0.00244; // equitorial paralalx in degree
+OA = 3956.6 ;//radius of earth
+angle_OAB = 90 ;//radius perpendicular to tangent
+OB = OA / sind(alpha) ;
+
+//ES is from earth surface to sun centre
+//centre of earth to sun is OB
+//we initially treated sun as point
+//that ditance is distance between their centres
+radius_earth=3956.6 ;//in miles
+ES = OB - radius_earth ;//in miles
+AS=ES * sind(angle_AES) ;//in miles
+printf('Required radius of sun = %.0f miles \n',AS)
+printf('Answer might vary due to approximations in book and scilab precision')
diff --git a/2915/CH1/EX1.17/1_17.JPG b/2915/CH1/EX1.17/1_17.JPG Binary files differnew file mode 100755 index 000000000..6ffad18ef --- /dev/null +++ b/2915/CH1/EX1.17/1_17.JPG diff --git a/2915/CH1/EX1.17/Ex1_17.sce b/2915/CH1/EX1.17/Ex1_17.sce new file mode 100755 index 000000000..45a6456d1 --- /dev/null +++ b/2915/CH1/EX1.17/Ex1_17.sce @@ -0,0 +1,35 @@ +clc,clear
+//Example 1.17
+//To find the diameter of larger roller
+
+//since radius perpendicular to tangent
+angle_ODA=90;
+angle_PEC=90
+angle_OAD=37 ;//by symmetry
+ED=1.38 ;//given
+//since DOA is right triangle, DOA and OAD are complementary angles
+angle_DOA=90 - angle_OAD ;
+
+//since radius perpendicular to tangent
+angle_OBC=90;
+angle_PBC=90;
+
+//since ODA and ODC are right triangle,
+//OD = OB as radius and BC=DC by pythagoras
+//OBC and ODC are now congruent
+//angle_BOC = angle_DOC
+//angle_BOC + angle_DOC =(90-angle_OAD)
+angle_BOC= (90-angle_OAD)/2;
+angle_DOC= (90-angle_OAD)/2;
+
+//BP=EP as radius
+//since radius perpendicular to tangent
+angle_PBC=90;
+angle_PEC=90;
+//Thus,BPC and EPC are congruent triangles
+//Therefore,BC=DC and BC+DC = ED
+BC = ED /2;
+DC = ED /2;
+OB = BC / tand(angle_BOC); //radius of large roller
+diameter= 2* OB ;
+printf('Diameter of larger roller = %.3f units',diameter)
diff --git a/2915/CH1/EX1.19/1_19.JPG b/2915/CH1/EX1.19/1_19.JPG Binary files differnew file mode 100755 index 000000000..ffffa475a --- /dev/null +++ b/2915/CH1/EX1.19/1_19.JPG diff --git a/2915/CH1/EX1.19/Ex1_19.sce b/2915/CH1/EX1.19/Ex1_19.sce new file mode 100755 index 000000000..7f5c5f118 --- /dev/null +++ b/2915/CH1/EX1.19/Ex1_19.sce @@ -0,0 +1,27 @@ +clc,clear
+//Example 1.19
+//To solve the right triangle with given information
+
+//part(a)
+c=10 ;//side opposite to vertex C
+A=22 ;//Angle at vertex A
+a=c*sind(A);
+b=c*cosd(A) ;
+B=90 - A ;//since C is 90, A and B are complimentary
+printf('(a)a= %.2f units ; b= %.2f units; B = %.0f degree\n',a,b,B)
+
+//part(b)
+b=8 ;//side opposite to vertex B
+A=40 ;//Angle at vertex A
+a=b*tand(A);
+c=b/cosd(A) ;
+B=90 - A ;//since C is 90, A and B are complimentary
+printf(' (b)a= %.2f units ; c= %.2f units; B = %.0f degree\n',a,c,B)
+
+//part(c)
+a=3 ;//side opposite to vertex A
+b=4 ;//side opposite to vertex B
+c=sqrt(a^2+b^2) ;//by pythagoras theorem
+A = atand(a/b) ;//angle at vertex A
+B=90 - A ;//since C is 90, A and B are complimentary
+printf(' (c)c=%.0f units ; A= %f degree; B = %f degree',c,A,B)
diff --git a/2915/CH1/EX1.20/1_20.JPG b/2915/CH1/EX1.20/1_20.JPG Binary files differnew file mode 100755 index 000000000..92eb1bf63 --- /dev/null +++ b/2915/CH1/EX1.20/1_20.JPG diff --git a/2915/CH1/EX1.20/Ex1_20.sce b/2915/CH1/EX1.20/Ex1_20.sce new file mode 100755 index 000000000..f8b7edb9e --- /dev/null +++ b/2915/CH1/EX1.20/Ex1_20.sce @@ -0,0 +1,27 @@ +clc,clear
+//Example 1.20
+//To find values of all trigonometric values of given angle of 120
+
+theta=120; //given angle in degree
+//Consider a point (-1,sqrt(3)) in 2nd quadrant
+//This point can be used on terminal side of 120
+//Thus for a basic right angled triangle formed in second quadrant
+adjacent = 1;
+opposite = sqrt(3);
+//by pythagoras theorem
+hypotenuse = sqrt(adjacent^2 + opposite^2);
+
+//since its third quadrant
+x=-adjacent;
+y= opposite;
+r=hypotenuse;
+
+sin_120 =y/r ;
+cos_120 =x/r ;
+tan_120 =y/x ;
+csc_120 =r/y ;
+sec_120 =r/x ;
+cot_120 =x/y ;
+
+printf('\nsin(%d)= %f ; cos(%d)= %f ; tan(%d)= %f ;',theta,sin_120,theta,cos_120,theta,tan_120)
+printf('\ncsc(%d)= %f ; sec(%d)= %f ; cot(%d)= %f ;',theta,csc_120,theta,sec_120,theta,cot_120)
diff --git a/2915/CH1/EX1.21/1_21.JPG b/2915/CH1/EX1.21/1_21.JPG Binary files differnew file mode 100755 index 000000000..cd0bb5632 --- /dev/null +++ b/2915/CH1/EX1.21/1_21.JPG diff --git a/2915/CH1/EX1.21/Ex1_21.sce b/2915/CH1/EX1.21/Ex1_21.sce new file mode 100755 index 000000000..fa30b4911 --- /dev/null +++ b/2915/CH1/EX1.21/Ex1_21.sce @@ -0,0 +1,27 @@ +clc,clear
+//Example 1.21
+//To find values of all trigonometric values of given angle of 225
+
+theta=225 ;//given angle in degree
+//Consider a point (-1,-1) in 3rd quadrant
+//This point can be used on terminal side of 225
+//Thus for a basic right angled triangle formed in 3rd quadrant
+adjacent = 1 ;
+opposite = 1 ;
+//by pythagoras theorem
+hypotenuse = sqrt(adjacent^2 + opposite^2) ;
+
+//since its third quadrant
+x=-adjacent ;
+y=-opposite ;
+r=hypotenuse ;
+
+sin_225 =y/r ;
+cos_225 =x/r ;
+tan_225 =y/x ;
+csc_225 =r/y ;
+sec_225 =r/x ;
+cot_225 =x/y ;
+
+printf('\nsin(%d)= %f ; cos(%d)= %f ; tan(%d)= %f ;',theta,sin_225,theta,cos_225,theta,tan_225)
+printf('\ncsc(%d)= %f ; sec(%d)= %f ; cot(%d)= %f ;',theta,csc_225,theta,sec_225,theta,cot_225)
diff --git a/2915/CH1/EX1.22/1_22.JPG b/2915/CH1/EX1.22/1_22.JPG Binary files differnew file mode 100755 index 000000000..696272525 --- /dev/null +++ b/2915/CH1/EX1.22/1_22.JPG diff --git a/2915/CH1/EX1.22/Ex1_22.sce b/2915/CH1/EX1.22/Ex1_22.sce new file mode 100755 index 000000000..5145e1530 --- /dev/null +++ b/2915/CH1/EX1.22/Ex1_22.sce @@ -0,0 +1,27 @@ +clc,clear
+//Example 1.22
+//To find values of all trigonometric values of given angle of 330
+
+theta=330 ; //given angle in degree
+//Consider a point (sqrt(3),-1) in 4th quadrant
+//This point can be used on terminal side of 330
+//Thus for a basic right angled triangle formed in 4th quadrant
+adjacent = sqrt(3);
+opposite = 1 ;
+hypotenuse = sqrt(adjacent^2 + opposite^2);
+//by pythagoras theorem
+
+//since its 4th quadrant
+x=adjacent ;
+y=-opposite ;
+r=hypotenuse ;
+
+sin_330 =y/r ;
+cos_330 =x/r ;
+tan_330 =y/x ;
+csc_330 =r/y ;
+sec_330 =r/x ;
+cot_330 =x/y ;
+
+printf('\nsin(%d)= %f ; cos(%d)= %f ; tan(%d)= %f ;',theta,sin_330,theta,cos_330,theta,tan_330)
+printf('\ncsc(%d)= %f ; sec(%d)= %f ; cot(%d)= %f ;',theta,csc_330,theta,sec_330,theta,cot_330)
diff --git a/2915/CH1/EX1.23/1_23.JPG b/2915/CH1/EX1.23/1_23.JPG Binary files differnew file mode 100755 index 000000000..3775f7f4c --- /dev/null +++ b/2915/CH1/EX1.23/1_23.JPG diff --git a/2915/CH1/EX1.23/Ex1_23.sce b/2915/CH1/EX1.23/Ex1_23.sce new file mode 100755 index 000000000..3fe81cd34 --- /dev/null +++ b/2915/CH1/EX1.23/Ex1_23.sce @@ -0,0 +1,89 @@ +clc,clear
+//Example 1.23
+//To find trigonometric functions of various angles
+//Note: Undefined ratios are commented to avoid divide by zero error
+
+//zero degrees
+//consider a point (1,0)
+//Line segment joining (0,0) and (1,0) can be treated as triangle
+
+x=1//base
+y=0//height
+r=1 //hypotenuse
+sin_0 = y/r;
+cos_0 = x/r;
+tan_0 = y/x;
+//csc_0 =r/y;
+sec_0 = r/x;
+//cot_0=x/y;
+printf('\nZERO DEGREES:\n')
+printf('sin(0)= %f;\n',sin_0)
+printf('cos(0)= %f;\n',cos_0)
+printf('tan(0)= %f;\n',tan_0)
+printf('csc(0)= undefined = (1/0);\n')
+printf('sec(0)= %f;\n',sec_0)
+printf('cot(0)= undefined = (1/0);\n')
+
+//90 degrees
+//consider a point (0,1)
+//Line segment joining (0,0) and (0,1) can be treated as triangle
+
+x=0//base
+y=1//height
+r=1 //hypotenuse
+sin_90 = y/r;
+cos_90 = x/r;
+//tan_90 = y/x;
+csc_90 =r/y;
+//sec_90 = r/x;
+cot_90=x/y;
+printf('\n90 DEGREES:\n')
+printf('sin(90)= %f;\n',sin_90)
+printf('cos(90)= %f;\n',cos_90)
+printf('tan(90)= undefined = (1/0);\n')
+printf('csc(90)= %f;\n',csc_90)
+printf('sec(90)= undefined = (1/0);\n')
+printf('cot(90)= %f;\n',cot_90)
+
+//180 degrees
+//consider a point (-1,0)
+//Line segment joining (0,0) and (-1,0) can be treated as triangle
+
+x=-1//base
+y=0//height
+r=1 //hypotenuse
+sin_180 = y/r;
+cos_180 = x/r;
+tan_180 = y/x;
+//csc_180 =r/y;
+sec_180 = r/x;
+//cot_180=x/y;
+printf('\n180 DEGREES:\n')
+printf('sin(180)= %f;\n',sin_180)
+printf('cos(180)= %f;\n',cos_180)
+printf('tan(180)= %f;\n',tan_180)
+printf('csc(180)= undefined = (1/0);\n')
+printf('sec(180)= %f;\n',sec_180)
+printf('cot(180)= undefined = (-1/0);\n')
+
+
+//270 degrees
+//consider a point (0,-1)
+//Line segment joining (0,0) and (0,-1) can be treated as triangle
+
+x=0//base
+y=-1//height
+r=1 //hypotenuse
+sin_270 = y/r;
+cos_270 = x/r
+//tan_90 = y/x;
+csc_270 =r/y;
+//sec_90 = r/x;
+cot_270=x/y;
+printf('\n270 DEGREES:\n')
+printf('sin(270)= %f;\n',sin_270)
+printf('cos(270)= %f;\n',cos_270)
+printf('tan(270)= undefined = (-1/0);\n')
+printf('csc(270)= %f;\n',csc_270)
+printf('sec(270)= undefined = (1/0);\n')
+printf('cot(270)= %f;\n',cot_270)
diff --git a/2915/CH1/EX1.24/1_24.JPG b/2915/CH1/EX1.24/1_24.JPG Binary files differnew file mode 100755 index 000000000..6e29988c2 --- /dev/null +++ b/2915/CH1/EX1.24/1_24.JPG diff --git a/2915/CH1/EX1.24/Ex1_24.sce b/2915/CH1/EX1.24/Ex1_24.sce new file mode 100755 index 000000000..cb991248a --- /dev/null +++ b/2915/CH1/EX1.24/Ex1_24.sce @@ -0,0 +1,21 @@ +clc,clear
+//Example 1.24
+//To determine reference angle and angle ( 0 to 360 )with same terminal side as given angle
+
+theta = 928 ;//given angle in degrees
+
+//The while loop works for ALL VALUES OF theta
+//It keeps subtracting 360 till a value in (0 to 360) is obtained
+ result = theta ;
+while 1==1,
+ if result<360 then
+ printf('(a)Required angel between 0 and 360 is %.0f degree',result);
+ break
+ end
+ result = result - 360 ;
+end
+
+//928 and 208 has same terminal side in 3rd quadrant
+//so their reference angle is same
+ref_angle_928 = result - 180 ; //required reference angle
+printf('\n(b)Reference angel for %.0f is %.0f degree',theta,ref_angle_928)
diff --git a/2915/CH1/EX1.25/1_25.JPG b/2915/CH1/EX1.25/1_25.JPG Binary files differnew file mode 100755 index 000000000..2da172eed --- /dev/null +++ b/2915/CH1/EX1.25/1_25.JPG diff --git a/2915/CH1/EX1.25/Ex1_25.sce b/2915/CH1/EX1.25/Ex1_25.sce new file mode 100755 index 000000000..034d727ad --- /dev/null +++ b/2915/CH1/EX1.25/Ex1_25.sce @@ -0,0 +1,26 @@ +clc,clear
+//Example 1.25
+//To find sin_theta and tan_theta when cos_theta is given
+
+cos_theta = -4/5;
+adjacent =4 ; hypotenuse =5 ;
+opposite = sqrt(hypotenuse ^2 - adjacent ^2) //by pythagoras theorem
+
+//minus sign of cos_theta implies 2nd or 3rd quadrant
+//Possibility 1 : 2nd quadrant
+x= -adjacent ;
+y= opposite ;
+r= hypotenuse ;
+sin_theta = y/r ;
+tan_theta = y/x ;
+printf('POSSIBILITY 1:Theta in 2nd quadrant\n')
+printf('sin(theta)= %.2f ; tan(theta) = %.2f; \n\n',sin_theta,tan_theta)
+
+//Possibility 2 : 3rd quadrant
+x=-adjacent ;
+y=-opposite ;
+r=hypotenuse ;
+sin_theta = y/r ;
+tan_theta = y/x ;
+printf('POSSIBILITY 2:Theta in 3rd quadrant\n')
+printf('sin(theta)= %.2f ; tan(theta) = %.2f; ',sin_theta,tan_theta)
diff --git a/2915/CH1/EX1.27/1_27.JPG b/2915/CH1/EX1.27/1_27.JPG Binary files differnew file mode 100755 index 000000000..d80ceb5dc --- /dev/null +++ b/2915/CH1/EX1.27/1_27.JPG diff --git a/2915/CH1/EX1.27/Ex1_27.sce b/2915/CH1/EX1.27/Ex1_27.sce new file mode 100755 index 000000000..c39436504 --- /dev/null +++ b/2915/CH1/EX1.27/Ex1_27.sce @@ -0,0 +1,13 @@ +clc,clear
+//Example 1.27
+//To find all the angles with a given sine function value
+
+sin_theta = -0.682;
+theta=asind(sin_theta);
+//This results -43 degree which isnt in 0 to 360 range
+//And theta exists in 4th quadrant
+//Angles in 1st and 2nd quadrant have +ve sine values
+
+theta1 = 180 - theta ;//reflection of theta in 3rd quadrant
+theta2 = 360 + theta ;//both theta n theta 2 have same trigonometric values
+printf('Required angles are %.0f and %.0f degrees',theta1,theta2)
diff --git a/2915/CH1/EX1.3/1_3.JPG b/2915/CH1/EX1.3/1_3.JPG Binary files differnew file mode 100755 index 000000000..0e0184b8b --- /dev/null +++ b/2915/CH1/EX1.3/1_3.JPG diff --git a/2915/CH1/EX1.3/Ex1_3.sce b/2915/CH1/EX1.3/Ex1_3.sce new file mode 100755 index 000000000..43e4f5ed8 --- /dev/null +++ b/2915/CH1/EX1.3/Ex1_3.sce @@ -0,0 +1,21 @@ +clc,clear
+//example 1.3
+//To determine length of unknown side in 3 given right triangles
+
+//Triangle ABC
+AB=5 //given
+AC=4 //given
+a=sqrt(AB^2- AC^2) //by pythagoras theorem
+printf('Triangle ABC: a=%f units \n',a)
+
+//Triangle DEF
+DE=2 //given
+EF=1 //given
+e=sqrt(DE^2- EF^2) //by pythagoras theorem
+printf(' Triangle DEF: e=%f units = sqrt(%f) units\n',e,e^2)
+
+//Triangle XYZ
+XZ=1 //given
+YZ=1 //given
+z=sqrt(XZ^2+YZ^2)//by pythagoras theorem
+printf(' Triangle XYZ: z=%f units = sqrt(%f) units\n',z,z^2)
diff --git a/2915/CH1/EX1.4/1_4.JPG b/2915/CH1/EX1.4/1_4.JPG Binary files differnew file mode 100755 index 000000000..b46170c32 --- /dev/null +++ b/2915/CH1/EX1.4/1_4.JPG diff --git a/2915/CH1/EX1.4/Ex1_4.sce b/2915/CH1/EX1.4/Ex1_4.sce new file mode 100755 index 000000000..3501070d6 --- /dev/null +++ b/2915/CH1/EX1.4/Ex1_4.sce @@ -0,0 +1,9 @@ +clc,clear
+//example 1.4
+//To determine height of the top of ladder touching the wall
+
+ladder = 17 //length of ladder or hypotenuse in feet
+base = 8 //distance between lower tip of ladder and wall in feet
+//Using pythagoras theorem
+h=sqrt(ladder^2 - base^2) //required height
+printf('Required height of top of ladder in contact with wall = %.0f ft',h)
diff --git a/2915/CH1/EX1.5/1_5.JPG b/2915/CH1/EX1.5/1_5.JPG Binary files differnew file mode 100755 index 000000000..1e37a2000 --- /dev/null +++ b/2915/CH1/EX1.5/1_5.JPG diff --git a/2915/CH1/EX1.5/Ex1_5.sce b/2915/CH1/EX1.5/Ex1_5.sce new file mode 100755 index 000000000..eac10f321 --- /dev/null +++ b/2915/CH1/EX1.5/Ex1_5.sce @@ -0,0 +1,33 @@ +clc,clear
+//example 1.5
+//To find values of all trigonometric functions for angles A and B
+
+//Angle at vertex A
+opposite = 3;
+adjacent = 4;
+hypotenuse=5;
+
+sin_A = opposite / hypotenuse;
+cos_A = adjacent / hypotenuse;
+tan_A = opposite / adjacent;
+csc_A = hypotenuse/opposite;
+sec_A = hypotenuse/adjacent;
+cot_A = adjacent / opposite;
+printf('ANGLE A')
+printf('\nsin(A)= %.1f ; cos(A)= %.2f; tan(A)= %.2f;\n',sin_A,cos_A,tan_A)
+printf('csc(A)= %.3f ; sec(A)= %.2f; cot(A)= %.2f;',csc_A,sec_A,cot_A)
+
+//Angle at vertex B
+opposite = 4;
+adjacent = 3;
+hypotenuse=5;
+
+sin_B = opposite / hypotenuse;
+cos_B = adjacent / hypotenuse;
+tan_B = opposite / adjacent;
+csc_B = hypotenuse/opposite;
+sec_B = hypotenuse/adjacent;
+cot_B = adjacent / opposite;
+printf('\n\nANGLE B')
+printf('\nsin(B)= %.1f ; cos(B)= %.2f; tan(B)= %.2f;\n',sin_B,cos_B,tan_B)
+printf('csc(B)= %.2f ; sec(B)= %.2f; cot(B)= %.2f;',csc_B,sec_B,cot_B)
diff --git a/2915/CH1/EX1.6/1_6.JPG b/2915/CH1/EX1.6/1_6.JPG Binary files differnew file mode 100755 index 000000000..5ce8a36e6 --- /dev/null +++ b/2915/CH1/EX1.6/1_6.JPG diff --git a/2915/CH1/EX1.6/Ex1_6.sce b/2915/CH1/EX1.6/Ex1_6.sce new file mode 100755 index 000000000..81fa6b5f4 --- /dev/null +++ b/2915/CH1/EX1.6/Ex1_6.sce @@ -0,0 +1,27 @@ +clc,clear
+//example 1.6
+//To find values of all trigonometric functions for 45 degree
+
+//Consider a square of side 1 and divide it half diagonally
+//ABC is now an isosceles triangle
+//angle A and B are now equal and = 45 degree
+
+AC=1;
+BC=1;
+AB=sqrt(AC^2+BC^2) //by pythagoras theorem
+c=AB //we denote AB by c as its opposite to C
+
+//conside angle BAC=45 degree
+opposite = BC;
+adjacent = AC;
+hypotenuse = c;
+sin_45 = opposite / hypotenuse;
+cos_45 = adjacent / hypotenuse;
+tan_45 = opposite / adjacent;
+csc_45 = hypotenuse/opposite;
+sec_45 = hypotenuse/adjacent;
+cot_45 = adjacent / opposite;
+
+printf('ANGLE = 45 degree')
+printf('\nsin(45)= %.4f ; cos(45)= %.4f; tan(45)= %.2f;\n',sin_45,cos_45,tan_45)
+printf('csc(45)= %.4f ; sec(45)= %.4f; cot(45)= %.2f;',csc_45,sec_45,cot_45)
diff --git a/2915/CH1/EX1.7/1_7.JPG b/2915/CH1/EX1.7/1_7.JPG Binary files differnew file mode 100755 index 000000000..8874b14b8 --- /dev/null +++ b/2915/CH1/EX1.7/1_7.JPG diff --git a/2915/CH1/EX1.7/Ex1_7.sce b/2915/CH1/EX1.7/Ex1_7.sce new file mode 100755 index 000000000..b2a959dfc --- /dev/null +++ b/2915/CH1/EX1.7/Ex1_7.sce @@ -0,0 +1,40 @@ +clc,clear
+//example 1.7
+//To find values of all trigonometric functions for 60 degree
+
+//take an equilateral triangle of side 2 and divide it by half
+//all 3 angles of equilateral triangle are same as 60 degree
+//the bisector of angle is also the perepndicual bisector of oppsoite side
+// Thus, A=60 B=30 C=90 in new triangle as shown in figure
+
+AB = 2; c=AB;
+AC = AB/2; b=AC;
+a=sqrt(c^2-b^2)//pythagoras theorem
+
+//For angle A=60 degree
+opposite = a;
+adjacent = b;
+hypotenuse = c;
+sin_60 = opposite / hypotenuse;
+cos_60 = adjacent / hypotenuse;
+tan_60 = opposite / adjacent;
+csc_60 = hypotenuse/opposite;
+sec_60 = hypotenuse/adjacent;
+cot_60 = adjacent / opposite;
+printf('ANGLE = 60 degree')
+printf('\nsin(60)= %.4f ; cos(60)= %.4f; tan(60)= %.4f;\n',sin_60,cos_60,tan_60)
+printf('csc(60)= %.4f ; sec(60)= %.4f; cot(60)= %.4f;',csc_60,sec_60,cot_60)
+
+//For angle ABC=30 degree
+opposite = b;
+adjacent = a;
+hypotenuse = c;
+sin_30 = opposite / hypotenuse;
+cos_30 = adjacent / hypotenuse;
+tan_30 = opposite / adjacent;
+csc_30 = hypotenuse/opposite;
+sec_30 = hypotenuse/adjacent;
+cot_30 = adjacent / opposite;
+printf('\n\nANGLE = 30 degree')
+printf('\nsin(30)= %.4f ; cos(30)= %.4f; tan(30)= %.4f;\n',sin_30,cos_30,tan_30)
+printf('csc(30)= %.4f ; sec(30)= %.4f; cot(30)= %.4f;',csc_30,sec_30,cot_30)
diff --git a/2915/CH1/EX1.8/1_8.JPG b/2915/CH1/EX1.8/1_8.JPG Binary files differnew file mode 100755 index 000000000..1389ed8f5 --- /dev/null +++ b/2915/CH1/EX1.8/1_8.JPG diff --git a/2915/CH1/EX1.8/Ex1_8.sce b/2915/CH1/EX1.8/Ex1_8.sce new file mode 100755 index 000000000..acd2641df --- /dev/null +++ b/2915/CH1/EX1.8/Ex1_8.sce @@ -0,0 +1,23 @@ +clc,clear
+//example 1.8
+//To find all trigonometric functions when sine functions is given
+
+sin_A=2/3 //given
+//since sine function is opposite/hypotenuse and
+//T-ratios are defined interms of ratio of sided of right triangle
+opposite=2;
+hypotenuse=3;
+BC = opposite;
+AB = hypotenuse;
+b = sqrt(hypotenuse^2- opposite^2) //by pythagoras theorem
+adjacent = b;
+
+cos_A = adjacent / hypotenuse;
+tan_A = opposite / adjacent;
+csc_A = hypotenuse/opposite;
+sec_A = hypotenuse/adjacent;
+cot_A = adjacent / opposite;
+
+printf('for ANGLE A')
+printf('\nsin(A)= %.4f ; cos(A)= %.4f; tan(A)= %.4f;\n',sin_A,cos_A,tan_A)
+printf('csc(A)= %.4f ; sec(A)= %.4f; cot(A)= %.4f;',csc_A,sec_A,cot_A)
diff --git a/2915/CH1/EX1.9/1_9.JPG b/2915/CH1/EX1.9/1_9.JPG Binary files differnew file mode 100755 index 000000000..8e3536b20 --- /dev/null +++ b/2915/CH1/EX1.9/1_9.JPG diff --git a/2915/CH1/EX1.9/Ex1_9.sce b/2915/CH1/EX1.9/Ex1_9.sce new file mode 100755 index 000000000..91d30465f --- /dev/null +++ b/2915/CH1/EX1.9/Ex1_9.sce @@ -0,0 +1,21 @@ +clc,clear
+//example 1.9
+//To convert given function into function of angle less than 45
+
+//(a)sin 65
+angle = 65 ;
+complement_angle = 90- 65 ;
+//cofuction of sine is cosine
+printf('(a)sin(%f)= cos (%f)\n',angle,complement_angle)
+
+//(b)cos 78
+angle = 78;
+complement_angle = 90- 78 ;
+//cofuction of cosine is sine
+printf('(b)cos(%f)= sin (%f)\n',angle,complement_angle)
+
+//(c)tan 59
+angle = 59 ;
+complement_angle = 90- 59 ;
+//cofuction of tan is cot
+printf('(c)tan(%f)= cot (%f)\n',angle,complement_angle)
diff --git a/2915/CH2/EX2.1/2_1.JPG b/2915/CH2/EX2.1/2_1.JPG Binary files differnew file mode 100755 index 000000000..3ef4e4ad9 --- /dev/null +++ b/2915/CH2/EX2.1/2_1.JPG diff --git a/2915/CH2/EX2.1/Ex2_1.sce b/2915/CH2/EX2.1/Ex2_1.sce new file mode 100755 index 000000000..c103039c8 --- /dev/null +++ b/2915/CH2/EX2.1/Ex2_1.sce @@ -0,0 +1,12 @@ +//Example 2.1
+//To solve the triangle when one side and 2 angles are given
+clc,clear
+
+a=10 //side opposite to vertex A
+A=41 //angle at vertex A
+C=75 //angle at vertex C
+
+B=180- (A+C)
+b=a*sind(B)/sind(A) //law of sines
+c=a*sind(C)/sind(A) //law of sines
+printf('Angle B is %.0f degrees\n length of side b is %.1f units\n length of side c is %.1f units',B,b,c)
diff --git a/2915/CH2/EX2.10/2_10.JPG b/2915/CH2/EX2.10/2_10.JPG Binary files differnew file mode 100755 index 000000000..d35db5255 --- /dev/null +++ b/2915/CH2/EX2.10/2_10.JPG diff --git a/2915/CH2/EX2.10/Ex2_10.sce b/2915/CH2/EX2.10/Ex2_10.sce new file mode 100755 index 000000000..fae4a483d --- /dev/null +++ b/2915/CH2/EX2.10/Ex2_10.sce @@ -0,0 +1,18 @@ +//Example 2.10
+//To solve the triangle when 2 sides and included angle is given
+clc,clear
+
+a=5 //side oposite to vertex a
+b=3 //side opposite to vertex b
+C=96 //angle at vertex C
+
+ApB=180-C //A + B
+//using law of tangents
+ AmB =2* atand( tand(ApB/2)*(a-b)/(a+b) ) //A-B
+
+//solving for A and B using AmB and ApB
+A= (AmB + ApB)/2
+B= ApB - A
+
+c=a*sind(C)/sind(A) //law of sines
+printf('Angle A= %.1f degree\nAngle B=%.1f degree\nlength of c=%.2f units',A,B,c)
diff --git a/2915/CH2/EX2.11/Ex2_11.sce b/2915/CH2/EX2.11/Ex2_11.sce new file mode 100755 index 000000000..b4f0bf036 --- /dev/null +++ b/2915/CH2/EX2.11/Ex2_11.sce @@ -0,0 +1,19 @@ +//Example 2.11
+//To check the solution of triangle using Mollweide equation
+clc,clear
+
+c=6.09 //side oposite to vertex C
+a=5 //side opposite to vertex A
+b=3 //side opposite to vertex B
+
+A=54.7 //angle at vertex A
+B=29.3 //angle at vertex B
+C=96 //angle at vertex C
+
+LHS = (a-b)/c
+RHS = sind((A-B)/2)/cosd(C/2)
+printf(' LHS = (a-b)/c = %.4f\n',LHS)
+printf(' RHS = sin((A-B)/2)/cos(C/2) = %.4f\n\n',RHS)
+
+printf('Small difference in LHS and RHS is due to rounding off.\ni.e.Mollweides equation is holding true.\n')
+printf('THE SOLUTION OF TRIANGLE IS CORRECT')
diff --git a/2915/CH2/EX2.12/Ex2_12.sce b/2915/CH2/EX2.12/Ex2_12.sce new file mode 100755 index 000000000..8ac62c25e --- /dev/null +++ b/2915/CH2/EX2.12/Ex2_12.sce @@ -0,0 +1,21 @@ +//Example 2.12
+//To determine if a triangle can be formed with given dimension
+clc,clear
+
+c=9 //side oposite to vertex C
+a=6 //side opposite to vertex A
+b=7 //side opposite to vertex B
+
+A=55 //angle at vertex A
+B=60 //angle at vertex B
+C=65 //angle at vertex C
+printf('Sum of angles=180\n')
+printf('Smallest and largest sides are opposite to smallest and largest angle respectively\n\n')
+
+LHS = (a+b)/c
+RHS = cosd((A-B)/2)/sind(C/2)
+printf(' LHS = (a+b)/c = %.2f\n',LHS)
+printf(' RHS = cos((A-B)/2)/sin(C/2) = %.2f\n\n',RHS)
+
+printf('As we can see, LHS is not equal to RHS.\ni.e.Mollweides equation is not holding true.\n')
+printf('THE TRIANGLE IS NOT POSSIBLE WITH GIVEN DIMENSIONS')
diff --git a/2915/CH2/EX2.13/2_13.JPG b/2915/CH2/EX2.13/2_13.JPG Binary files differnew file mode 100755 index 000000000..d0a919259 --- /dev/null +++ b/2915/CH2/EX2.13/2_13.JPG diff --git a/2915/CH2/EX2.13/Ex2_13.sce b/2915/CH2/EX2.13/Ex2_13.sce new file mode 100755 index 000000000..291a767d3 --- /dev/null +++ b/2915/CH2/EX2.13/Ex2_13.sce @@ -0,0 +1,10 @@ +//Example 2.13
+//To determine area of triangle when 2 sides and an angle is given
+clc,clear
+
+c=7 //side oposite to vertex C
+A=33 //angle at vertex A
+b=5 //side opposite to vertex B
+
+area_K = b*c*sind(A)/2
+printf('Area of triangle ABC = %.2f square units',area_K)
diff --git a/2915/CH2/EX2.14/2_14.JPG b/2915/CH2/EX2.14/2_14.JPG Binary files differnew file mode 100755 index 000000000..f70abaed1 --- /dev/null +++ b/2915/CH2/EX2.14/2_14.JPG diff --git a/2915/CH2/EX2.14/Ex2_14.sce b/2915/CH2/EX2.14/Ex2_14.sce new file mode 100755 index 000000000..e82ffe556 --- /dev/null +++ b/2915/CH2/EX2.14/Ex2_14.sce @@ -0,0 +1,11 @@ +//Example 2.14
+//To determine area of triangle when 3 angles and a side is given
+clc,clear
+
+A=115 //angle at vertex A
+a=12 //side opposite to vertex A
+B=25 //angle at vertex B
+C=40 //angle at vertex C
+
+area_K = a^2*sind(B)*sind(C)/(2*sind(A))
+printf('Area of triangle ABC = %.2f square units',area_K)
diff --git a/2915/CH2/EX2.15/2_15.JPG b/2915/CH2/EX2.15/2_15.JPG Binary files differnew file mode 100755 index 000000000..df7bfb3c3 --- /dev/null +++ b/2915/CH2/EX2.15/2_15.JPG diff --git a/2915/CH2/EX2.15/Ex2_15.sce b/2915/CH2/EX2.15/Ex2_15.sce new file mode 100755 index 000000000..cbb54699f --- /dev/null +++ b/2915/CH2/EX2.15/Ex2_15.sce @@ -0,0 +1,11 @@ +//Example 2.15
+//To determine area of triangle when 3 sides are given
+clc,clear
+
+c=7 //side oposite to vertex C
+a=5 //side opposite to vertex A
+b=4 //side opposite to vertex B
+
+s= (a+b+c)/2 //semi perimeter
+area_K = sqrt(s*(s-a)*(s-b)*(s-c)) //using herons formula
+printf('Area of triangle ABC = %.2f square units',area_K)
diff --git a/2915/CH2/EX2.16/Ex2_16.sce b/2915/CH2/EX2.16/Ex2_16.sce new file mode 100755 index 000000000..9495fe727 --- /dev/null +++ b/2915/CH2/EX2.16/Ex2_16.sce @@ -0,0 +1,16 @@ +//Example 2.16
+//To determine area of triangle when 3 sides are given
+clc,clear
+
+c=0.0000029 //side oposite to vertex C
+a=1000000 //side opposite to vertex A
+b=999999.9999979 //side opposite to vertex B
+
+s= (a+b+c)/2 //semi perimeter
+area_K = sqrt(s*(s-a)*(s-b)*(s-c)) //using herons formula
+printf('Area of triangle ABC = %.3f square units\n\n',area_K)
+
+printf('Note:\n')
+printf('In calculators like TI-83 plus, due to rounding off etc s will be 1000000\n')
+printf('Therefore (s-a) is zero. And area will be zero according to herons formula\n')
+printf('Due to large number of digits in scilab,(s-a) is not zero. Thus, area is non-zero above.')
diff --git a/2915/CH2/EX2.17/2_17.JPG b/2915/CH2/EX2.17/2_17.JPG Binary files differnew file mode 100755 index 000000000..9032ba2be --- /dev/null +++ b/2915/CH2/EX2.17/2_17.JPG diff --git a/2915/CH2/EX2.17/Ex2_17.sce b/2915/CH2/EX2.17/Ex2_17.sce new file mode 100755 index 000000000..bf2a15c0b --- /dev/null +++ b/2915/CH2/EX2.17/Ex2_17.sce @@ -0,0 +1,14 @@ +//Example 2.17
+//To find radius of circumscribed circle for triangle ABC
+clc,clear
+
+c=5//side oposite to vertex C
+a=3//side opposite to vertex A
+b=4//side opposite to vertex B
+
+cos_A = (c^2+b^2-a^2)/(2*c*b) //from law of cosines
+A= acosd(cos_A)
+diameter=(a/sind(A))
+radius = diameter/2
+printf('Radius of circumscribed circle = %.1f units \n',radius)
+printf('\nNote :\n Diameter is same as AB i.e. c... So centre of circle is mipoint of AB')
diff --git a/2915/CH2/EX2.18/2_18.JPG b/2915/CH2/EX2.18/2_18.JPG Binary files differnew file mode 100755 index 000000000..0beecf0f0 --- /dev/null +++ b/2915/CH2/EX2.18/2_18.JPG diff --git a/2915/CH2/EX2.18/Ex2_18.sce b/2915/CH2/EX2.18/Ex2_18.sce new file mode 100755 index 000000000..a08b4578c --- /dev/null +++ b/2915/CH2/EX2.18/Ex2_18.sce @@ -0,0 +1,26 @@ +//Example 2.18
+//To find the radius of circumscribed circle for triangle ABC
+clc,clear
+
+c=4 //side oposite to vertex C
+a=2 //side opposite to vertex A
+b=3 //side opposite to vertex B
+
+cos_A = (c^2+b^2-a^2)/(2*c*b) //from law of cosines
+A= acosd(cos_A)
+diameter=(a/sind(A))
+radius = diameter/2
+printf('Radius of circumscribed circle = %.2f units \n\n',radius)
+
+//To draw the triangle
+printf('NOTE:\nPROCEDURE TO DRAW THE TRIANGLE ABC\n')
+printf('Use a ruler to draw the longest side AB of length c = 4.\n')
+printf('Use a compass to draw arcs of radius 3 and 2 centered at A and B respectively.\n')
+printf('The intersection of the arcs is the vertex C.\n\n')
+
+//To draw the circumscribed circle
+printf('PROCEDURE TO DRAW CIRCUMSCRIBED CIRCLE\n')
+printf('Draw the perpendicular bisectors of AB and AC.\n')
+printf('Their intersection is the center O of the circle.\n')
+printf('Use a compass to draw the circle centered at O which passes through A.')
+
diff --git a/2915/CH2/EX2.19/2_19.JPG b/2915/CH2/EX2.19/2_19.JPG Binary files differnew file mode 100755 index 000000000..666fb654d --- /dev/null +++ b/2915/CH2/EX2.19/2_19.JPG diff --git a/2915/CH2/EX2.19/Ex2_19.sce b/2915/CH2/EX2.19/Ex2_19.sce new file mode 100755 index 000000000..1d97ee5bf --- /dev/null +++ b/2915/CH2/EX2.19/Ex2_19.sce @@ -0,0 +1,15 @@ +//Example 2.19
+//To determine radius of inscribed circle ABC
+clc,clear
+
+c=4 //side oposite to vertex C
+a=2 //side opposite to vertex A
+b=3 //side opposite to vertex B
+
+s= (a+b+c)/2 //semi perimeter
+radius_r = sqrt((s-a)*(s-b)*(s-c)/s)
+printf('Radius of inscribed circle is %.3f units= sqrt(5/12)units ',radius_r)
+printf('\n\nNote:To obtain inscribed circle:\n(1)Intersect perpendicular bisectors of A and B\n')
+printf('(2)Point of intersection is the centre of circle\n')
+printf('(3)The radius is 0.645 as caculated above\n')
+printf('(4)Using a compass draw a circle with this centre\n')
diff --git a/2915/CH2/EX2.2/2_2.JPG b/2915/CH2/EX2.2/2_2.JPG Binary files differnew file mode 100755 index 000000000..3774b46e0 --- /dev/null +++ b/2915/CH2/EX2.2/2_2.JPG diff --git a/2915/CH2/EX2.2/Ex2_2.sce b/2915/CH2/EX2.2/Ex2_2.sce new file mode 100755 index 000000000..202d0708d --- /dev/null +++ b/2915/CH2/EX2.2/Ex2_2.sce @@ -0,0 +1,21 @@ +//Example 2.2
+//To solve the triangle when 2 sides and one opposite angle is given
+clc,clear
+
+a=18 //side oposite to vertex A
+A=25 //angle at vertex A
+b=30 //side opposite to vertex B
+
+sin_B=(b/a)*sind(A) //law of sines
+
+//case 1
+B=asind(sin_B) //law of sines
+C=180-(A+B)
+c=a*sind(C)/sind(A) //law of sines
+printf('1st possible solution set\nAngle at B =%.1f degree\nAngle at C=%.1f degree\nlength of side c=%.0f units\n',B,C,c)
+
+//case 2
+B=180 - asind(sin_B) //law of sines
+C=180-(A+B)
+c=a*sind(C)/sind(A) //law of sines
+printf('\n\n2nd possible solution set\nAngle at B =%.1f degree\nAngle at C=%.1f degree\nlength of side c=%.1f units\n',B,C,c)
diff --git a/2915/CH2/EX2.3/Ex2_3.sce b/2915/CH2/EX2.3/Ex2_3.sce new file mode 100755 index 000000000..47377dd00 --- /dev/null +++ b/2915/CH2/EX2.3/Ex2_3.sce @@ -0,0 +1,10 @@ +//Example 2.3
+//To solve the triangle when 2 sides and opposite angle is given
+clc,clear
+
+a=5 //side oposite to vertex A
+A=30 //angle at vertex A
+b=12 //side opposite to vertex B
+
+sin_B=(b/a)*sind(A) //law of sines
+printf("sin(B)=%f. But magnitude of sin(B) should be less than 1\nHence,there is no solution",sin_B)
diff --git a/2915/CH2/EX2.4/2_4.JPG b/2915/CH2/EX2.4/2_4.JPG Binary files differnew file mode 100755 index 000000000..196f68671 --- /dev/null +++ b/2915/CH2/EX2.4/2_4.JPG diff --git a/2915/CH2/EX2.4/Ex2_4.sce b/2915/CH2/EX2.4/Ex2_4.sce new file mode 100755 index 000000000..bf69fe635 --- /dev/null +++ b/2915/CH2/EX2.4/Ex2_4.sce @@ -0,0 +1,14 @@ +//Example 2.4
+//To solve the triangle when 2 sides and angle between them is given
+clc,clear
+
+c=5 //side oposite to vertex C
+A=30 //angle at vertex A
+b=4 //side opposite to vertex B
+
+printf('By law of sines:\n')
+printf('a/sin(30) = 4/sin(B) = 5 / sin(C)\n')
+printf('\nEach of the equations has 2 unknowns.')
+printf('\nFor eg: To obtain a , we can use 4/sin(B)=5/sin(C). Next we obtain B interms of C and put back.\n')
+printf('Now we have a in terms of C which is unknown\n')
+printf('Hence it is IMPOSSIBLE to solve this by law of sines')
diff --git a/2915/CH2/EX2.5/2_5.JPG b/2915/CH2/EX2.5/2_5.JPG Binary files differnew file mode 100755 index 000000000..407123a8a --- /dev/null +++ b/2915/CH2/EX2.5/2_5.JPG diff --git a/2915/CH2/EX2.5/Ex2_5.sce b/2915/CH2/EX2.5/Ex2_5.sce new file mode 100755 index 000000000..6cf14ba11 --- /dev/null +++ b/2915/CH2/EX2.5/Ex2_5.sce @@ -0,0 +1,15 @@ +//Example 2.5
+//To solve the triangle when 2 sides and angle between them is given
+clc,clear
+
+c=5 //side oposite to vertex C
+A=30 //angle at vertex A
+b=4 //side opposite to vertex B
+
+a = sqrt( b^2 + c^2 -2*b*c*cosd(A) ) //from law of cosines
+printf('Length of a= %.2f units\n',a)
+cos_B = (c^2+a^2-b^2)/(2*c*a) //from law of cosines
+B=acosd(cos_B)
+printf('Angle B=%.1f degrees\n',B)
+C=180-(A+B)
+printf('Angle C=%.1f degrees\n',C)
diff --git a/2915/CH2/EX2.6/2_6.JPG b/2915/CH2/EX2.6/2_6.JPG Binary files differnew file mode 100755 index 000000000..e398d1166 --- /dev/null +++ b/2915/CH2/EX2.6/2_6.JPG diff --git a/2915/CH2/EX2.6/Ex2_6.sce b/2915/CH2/EX2.6/Ex2_6.sce new file mode 100755 index 000000000..e668c2e32 --- /dev/null +++ b/2915/CH2/EX2.6/Ex2_6.sce @@ -0,0 +1,17 @@ +//Example 2.6
+//To solve the triangle when 3 sides are given
+clc,clear
+
+c=4 //side oposite to vertex C
+a=2 //side opposite to vertex A
+b=3 //side opposite to vertex B
+
+cos_B = (c^2+a^2-b^2)/(2*c*a) //from law of cosines
+B=acosd(cos_B)
+printf('Angle B=%.1f degrees\n',B)
+cos_C = (b^2+a^2-c^2)/(2*b*a) //from law of cosines
+C=acosd(cos_C)
+printf('Angle C=%.1f degrees\n',C)
+
+A=180-(C+B)
+printf('Angle A=%f degrees',A)
diff --git a/2915/CH2/EX2.7/2_7.JPG b/2915/CH2/EX2.7/2_7.JPG Binary files differnew file mode 100755 index 000000000..ce320f11a --- /dev/null +++ b/2915/CH2/EX2.7/2_7.JPG diff --git a/2915/CH2/EX2.7/Ex2_7.sce b/2915/CH2/EX2.7/Ex2_7.sce new file mode 100755 index 000000000..3bfad5c0e --- /dev/null +++ b/2915/CH2/EX2.7/Ex2_7.sce @@ -0,0 +1,14 @@ +//Example 2.7
+//To determine solution of a triangle when 3 sides are given
+clc,clear
+
+c=6 //side oposite to vertex C
+a=2 //side opposite to vertex A
+b=3 //side opposite to vertex B
+
+cos_A = (b^2+c^2-a^2)/(2*c*b) //from law of cosines
+printf('cos(A)=%.3f as calculated\n',cos_A)
+printf('But magnitude of cos(A) should always be less than 1. Hence NO SOLUTION exists\n\n')
+
+printf('Note: We observe that a+b < c. But sum of any 2 sides should always exceed third side.')
+printf('\nHence this triangle is impossible.')
diff --git a/2915/CH2/EX2.8/Ex2_8.sce b/2915/CH2/EX2.8/Ex2_8.sce new file mode 100755 index 000000000..eaf45f6a4 --- /dev/null +++ b/2915/CH2/EX2.8/Ex2_8.sce @@ -0,0 +1,25 @@ +//Example 2.8
+//To solve the triangle when 2 sides and opposite angle is given
+clc,clear
+
+a=18 //side oposite to vertex A
+A=25 //angle at vertex A
+b=30 //side opposite to vertex B
+
+//using law of cosines solving for c
+c_polynomial=[1 -54.38 576]
+root_c=roots(c_polynomial)
+
+//case 1
+c=root_c(1)
+cos_B = (c^2+a^2-b^2)/(2*c*a) //from law of cosines
+B= (180/%pi)*acos (cos_B)
+C=180-(A+B)
+printf('1st possible answer set\nAngle B=%.1f degree\nAngle C=%.1f degree\nlength of c=%.0f units\n\n',B,C,c)
+
+//case 2
+c=root_c(2)
+cos_B = (c^2+a^2-b^2)/(2*c*a) //from law of cosines
+B=(180/%pi)*acos(cos_B)
+C=180-(A+B)
+printf('2nd possible answer set(which is not solved in book)\nAngle B=%.1f degree\nAngle C=%.1f degree\nlength of c=%.0f units\n',B,C,c)
diff --git a/2915/CH3/EX3.8/Ex3_8.sce b/2915/CH3/EX3.8/Ex3_8.sce new file mode 100755 index 000000000..b1b28b100 --- /dev/null +++ b/2915/CH3/EX3.8/Ex3_8.sce @@ -0,0 +1,18 @@ +clc,clear
+//Example 3.8
+//To determine values of functions of sum of 2 angles when functions of 2 angles are given
+
+sin_A = 4/5 ;
+cos_A = 3/5 ;
+
+sin_B = 12/13 ;
+cos_B = 5/13 ;
+
+//Apb refers to A plus B
+sin_ApB = sin_A*cos_B + cos_A*sin_B ;
+cos_ApB = cos_A*cos_B - sin_A*sin_B ;
+tan_ApB = sin_ApB / cos_ApB ;
+
+printf('sin(A+B) = %f\n',sin_ApB) ;
+printf('cos(A+B) = %f\n',cos_ApB) ;
+printf('tan(A+B) = %f\n',tan_ApB) ;
diff --git a/2915/CH4/EX4.1/Ex4_1.sce b/2915/CH4/EX4.1/Ex4_1.sce new file mode 100755 index 000000000..b3eef3e0d --- /dev/null +++ b/2915/CH4/EX4.1/Ex4_1.sce @@ -0,0 +1,9 @@ +clc,clear
+//Example 4.1
+//To convert a degree measure to radians
+
+deg=18 //degree measure
+radian=deg*(%pi/180) //radian measure
+printf('Radian measure is %f rad\n(or)\n',radian)
+printf('Radian measure is (pi/%.0f)rad',1/(radian/%pi))
+
diff --git a/2915/CH4/EX4.10/Ex4_10.sce b/2915/CH4/EX4.10/Ex4_10.sce new file mode 100755 index 000000000..bd754b8e1 --- /dev/null +++ b/2915/CH4/EX4.10/Ex4_10.sce @@ -0,0 +1,9 @@ +clc,clear
+//Example 4.10
+//To determine area of sector of circle
+
+s=6 //arc length in cm
+r=9 //radius in cm
+A=r*s/2 //Area of sector
+printf('Area of sector = %.0f cm^2\n\n',A)
+printf('Note: Angle subtended by arc = %f rad',s/r)
diff --git a/2915/CH4/EX4.11/4_11.JPG b/2915/CH4/EX4.11/4_11.JPG Binary files differnew file mode 100755 index 000000000..c547a9f21 --- /dev/null +++ b/2915/CH4/EX4.11/4_11.JPG diff --git a/2915/CH4/EX4.11/Ex4_11.sce b/2915/CH4/EX4.11/Ex4_11.sce new file mode 100755 index 000000000..cee1e209f --- /dev/null +++ b/2915/CH4/EX4.11/Ex4_11.sce @@ -0,0 +1,27 @@ +clc,clear
+//Example 4.11
+//To determine area insude belt pulley system
+
+AE= 5 //radius of first pulley
+BF= 8 //radius of second pulley
+AB=15 //distance between centre of pulleys
+
+//from the figure
+CF=AE
+BC= BF- CF
+AC = sqrt(AB^2 - BC^2)
+//from the figure
+angle_EAC = %pi/2
+angle_BAC = asin(BC/AB)
+angle_DAE = %pi - angle_EAC - angle_BAC
+angle_ABC = angle_DAE //AE and BF are parallel
+angle_GBF= %pi - angle_ABC
+
+area_DAE = AE^2*angle_DAE/2 //area of sector DAE
+area_GBF = BF^2*angle_GBF/2 //area of sector GBF
+area_AEFC = AE*AC //area of rectangle AEFC
+area_ABC = AC*BC/2 //area of triangle ABC
+
+area_K=2*(area_DAE + area_AEFC + area_ABC + + area_GBF )
+printf('Area enclosed by belt pulley system = %.2f cm^2',area_K)
+printf('\n\nNote: answer differs from book due to approximations by them')
diff --git a/2915/CH4/EX4.12/4_12.JPG b/2915/CH4/EX4.12/4_12.JPG Binary files differnew file mode 100755 index 000000000..4f68d8eb5 --- /dev/null +++ b/2915/CH4/EX4.12/4_12.JPG diff --git a/2915/CH4/EX4.12/Ex4_12.sce b/2915/CH4/EX4.12/Ex4_12.sce new file mode 100755 index 000000000..dd879f272 --- /dev/null +++ b/2915/CH4/EX4.12/Ex4_12.sce @@ -0,0 +1,12 @@ +clc,clear
+//Example 4.12
+//To determine area of segment formed by a chord in circle
+
+radius = 2
+chord = 3
+//Use law of cosines
+cos_theta = (radius^2+radius^2-chord^2)/(2*radius*radius)
+theta=acos(cos_theta) //subtended central angle in radians
+
+area_K=radius^2* (theta-sin(theta))/2
+printf('Required area of segment = %.3f square units',area_K)
diff --git a/2915/CH4/EX4.13/4_13.JPG b/2915/CH4/EX4.13/4_13.JPG Binary files differnew file mode 100755 index 000000000..df9c550ab --- /dev/null +++ b/2915/CH4/EX4.13/4_13.JPG diff --git a/2915/CH4/EX4.13/Ex4_13.sce b/2915/CH4/EX4.13/Ex4_13.sce new file mode 100755 index 000000000..a061e3fc0 --- /dev/null +++ b/2915/CH4/EX4.13/Ex4_13.sce @@ -0,0 +1,24 @@ +clc,clear
+//Example 4.13
+//To determine area of intersection of 2 circles
+
+d=7 //distance between centres in cm
+r1= 5 //radius of first circle in cm
+r2= 4 //radius of second circle in cm
+
+//use law of cosines
+cos_alpha=(d^2+ r1^2 - r2^2 ) /(2*d*r1)
+cos_beeta=(d^2+ r2^2 - r1^2 ) /(2*d*r2)
+
+//from the geometry of the figure
+//all the angles below are in radians
+alpha= acos(cos_alpha)
+beeta= acos(cos_beeta)
+angle_BAC = alpha
+angle_ABC = beeta
+angle_CAD =2* angle_BAC
+angle_CBD =2* angle_ABC
+
+//required area = area at segment CD in circle at A and at B
+area_K = r1^2*(angle_CAD-sin(angle_CAD))/2 + r2^2*(angle_CBD-sin(angle_CBD))/2
+printf('Area of intersection of 2 circles = %.2f cm^2',area_K)
diff --git a/2915/CH4/EX4.14/Ex4_14.sce b/2915/CH4/EX4.14/Ex4_14.sce new file mode 100755 index 000000000..bd8fbc541 --- /dev/null +++ b/2915/CH4/EX4.14/Ex4_14.sce @@ -0,0 +1,15 @@ +clc,clear
+//Example 4.14
+//To find linear and angular speed of a moving object
+
+t=0.5 //time in second
+r= 3 //radius in m of the circle
+theta = %pi/3 // central angle in radian
+w = theta/t //angular speed in rad /sec
+v=w*r//linear speed in m/sec
+
+printf('Angular speed= %f radian/sec\n',w)
+printf('Linear speed = %f m/sec',v)
+
+printf('\n\n(or)\n\nAngular speed= %f*pi radian/sec\n',w/%pi)
+printf('Linear speed = %f*pi m/sec',v/%pi)
diff --git a/2915/CH4/EX4.15/Ex4_15.sce b/2915/CH4/EX4.15/Ex4_15.sce new file mode 100755 index 000000000..eaabe733b --- /dev/null +++ b/2915/CH4/EX4.15/Ex4_15.sce @@ -0,0 +1,13 @@ +clc,clear
+//Example 4.15
+//To find linear and angular speed of a moving object
+
+t=2.7 //time in second
+r= 2 //radius in ft of the circle
+s=35 //distance in feet
+
+v=s/t //linear speed in ft/sec
+w=v/r //angular speed in rad /sec
+
+printf('Linear speed = %.2f ft/sec\n',v)
+printf('Angular speed= %.2f radian/sec\n',w)
diff --git a/2915/CH4/EX4.16/Ex4_16.sce b/2915/CH4/EX4.16/Ex4_16.sce new file mode 100755 index 000000000..95a75ff15 --- /dev/null +++ b/2915/CH4/EX4.16/Ex4_16.sce @@ -0,0 +1,11 @@ +clc,clear
+//Example 4.16
+//To find the central angle swept by a moving object
+
+t=3.1 //time in second
+v= 10 //linear speed in m/sec
+r= 4 //radius in m of the circle
+s=v*t //distance in m
+
+theta = s/r //central angle swept
+printf('central angle swept = %.2f radian',theta)
diff --git a/2915/CH4/EX4.17/4_17.JPG b/2915/CH4/EX4.17/4_17.JPG Binary files differnew file mode 100755 index 000000000..ef7bf12fc --- /dev/null +++ b/2915/CH4/EX4.17/4_17.JPG diff --git a/2915/CH4/EX4.17/Ex4_17.sce b/2915/CH4/EX4.17/Ex4_17.sce new file mode 100755 index 000000000..2165319b3 --- /dev/null +++ b/2915/CH4/EX4.17/Ex4_17.sce @@ -0,0 +1,15 @@ +clc,clear
+//Example 4.17
+//To find the angular speed of larger gear interlocked with smaller gear
+
+r1=5 //radius of larger gear
+r2=4 //radius smaller gear
+w2=25 //angular speed of smaller gear
+
+// Imagine a particle on outer radii of each gear
+//At any time, for every rotation, circular displacement of each particle is same
+// (or) s1=s2 implies v1*t=v2*t
+//v1= v2 implies w1*r1=w2*r2
+
+w1=(w2*r2)/r1 //angular speed of larger gear
+printf('Angular speed of larger gear= %.0f rpm ',w1)
diff --git a/2915/CH4/EX4.2/Ex4_2.sce b/2915/CH4/EX4.2/Ex4_2.sce new file mode 100755 index 000000000..e88a0ad66 --- /dev/null +++ b/2915/CH4/EX4.2/Ex4_2.sce @@ -0,0 +1,7 @@ +clc,clear
+//Example 4.2
+//To convert a radian meeasure to degree
+
+radian=%pi/9 //radian measure
+deg=radian/(%pi/180) //degree measure
+printf('Degree measure is %.0f degree',deg)
diff --git a/2915/CH4/EX4.3/Ex4_3.sce b/2915/CH4/EX4.3/Ex4_3.sce new file mode 100755 index 000000000..3da6be6b6 --- /dev/null +++ b/2915/CH4/EX4.3/Ex4_3.sce @@ -0,0 +1,9 @@ +clc,clear
+//Example 4.3
+//To determine length of the intercepted arc
+
+r=2 //radius of circle
+theta=1.2 //central angle in radian
+
+s=r*theta //length of arc
+printf('Length of arc intercepted = %.1f cm',s)
diff --git a/2915/CH4/EX4.4/Ex4_4.sce b/2915/CH4/EX4.4/Ex4_4.sce new file mode 100755 index 000000000..7f58dc681 --- /dev/null +++ b/2915/CH4/EX4.4/Ex4_4.sce @@ -0,0 +1,9 @@ +clc,clear
+//Example 4.4
+//To determine length of the arc intercepted
+
+r=10 //radius of circle
+theta=41*(%pi/180) //central angle in radian
+
+s=r*theta //length of arc
+printf('Length of arc intercepted = %.2f ft',s)
diff --git a/2915/CH4/EX4.5/Ex4_5.sce b/2915/CH4/EX4.5/Ex4_5.sce new file mode 100755 index 000000000..e20806793 --- /dev/null +++ b/2915/CH4/EX4.5/Ex4_5.sce @@ -0,0 +1,9 @@ +clc,clear
+//Example 4.5
+//To determine angle in radians and degrees
+
+r=5 //radius of circle
+s=2 //length of arc
+theta = s/r //central angle in radian
+printf('Measure of central angle = %.2f rad\n',theta)
+printf('Measure of central angle = %.2f degree',theta*(180/%pi))
diff --git a/2915/CH4/EX4.6/4_6.JPG b/2915/CH4/EX4.6/4_6.JPG Binary files differnew file mode 100755 index 000000000..99df9e3f9 --- /dev/null +++ b/2915/CH4/EX4.6/4_6.JPG diff --git a/2915/CH4/EX4.6/Ex4_6.sce b/2915/CH4/EX4.6/Ex4_6.sce new file mode 100755 index 000000000..d58da26f1 --- /dev/null +++ b/2915/CH4/EX4.6/Ex4_6.sce @@ -0,0 +1,20 @@ +clc,clear
+//Example 4.6
+//To determine the length of the rope
+
+d=8 //distance between places in feet
+r=2 //radius of cylinder in feet
+//from the figure
+DA=d/2,BE=r
+DE=3 //distance from centre of container to wall
+
+AE=sqrt(DE^2 + DA^2) //pythagoras theorem
+AB=sqrt(AE^2 - BE^2) //pythagoras theorem
+
+//all angles below are in radians
+angle_AED = atan((d/2)/DE)
+angle_AEB = acos(BE/AE)
+angle_BEC = %pi - (angle_AED + angle_AEB)
+arc_BC = BE*angle_BEC //length of arc BC
+L = 2*(AB + arc_BC) //length of rope
+printf('Length of the rope = %.1f ft',L)
diff --git a/2915/CH4/EX4.7/4_7.JPG b/2915/CH4/EX4.7/4_7.JPG Binary files differnew file mode 100755 index 000000000..eccc64728 --- /dev/null +++ b/2915/CH4/EX4.7/4_7.JPG diff --git a/2915/CH4/EX4.7/Ex4_7.sce b/2915/CH4/EX4.7/Ex4_7.sce new file mode 100755 index 000000000..e4cea151e --- /dev/null +++ b/2915/CH4/EX4.7/Ex4_7.sce @@ -0,0 +1,24 @@ +clc,clear
+//Example 4.7
+//To determine the length of the belt around the pulleys
+
+AE= 5 //radius of first pulley in cm
+BF= 8 //radius of second pulley in cm
+AB=15 //distance between centre of pulleys in cm
+
+//from the figure
+CF=AE //parallel side of rectangle ACFE
+BC= BF- CF
+AC = sqrt(AB^2 - BC^2) //by pythagoras theorem
+EF=AC//parallel side of rectangle ACFE
+
+angle_EAC = %pi/2
+angle_BAC = asin(BC/AB)
+angle_DAE = %pi - angle_EAC - angle_BAC
+angle_ABC = angle_DAE //AE and BF are parallel
+angle_GBF= %pi - angle_ABC
+
+arc_DE=AE*angle_ABC //length of arc DE
+arc_FG=BF*angle_GBF //length of arc FG
+L=2*(arc_DE + EF + arc_FG) //length of belt
+printf('Length of belt around pulley = %f cm',L)
diff --git a/2915/CH4/EX4.8/Ex4_8.sce b/2915/CH4/EX4.8/Ex4_8.sce new file mode 100755 index 000000000..5e8336c63 --- /dev/null +++ b/2915/CH4/EX4.8/Ex4_8.sce @@ -0,0 +1,9 @@ +clc,clear
+//Example 4.8
+//To find the area of sector of circle
+
+theta= %pi/5 //angle in radian
+r=4 //radius in cm
+A=r*r*theta/2 //Area of sector
+printf('Area of sector = %.1f*pi cm^2\n(or)\n',A/%pi)
+printf('Area of sector = %f cm^2',A)
diff --git a/2915/CH4/EX4.9/Ex4_9.sce b/2915/CH4/EX4.9/Ex4_9.sce new file mode 100755 index 000000000..b53119078 --- /dev/null +++ b/2915/CH4/EX4.9/Ex4_9.sce @@ -0,0 +1,8 @@ +clc,clear
+//Example 4.9
+//To determine area of sector of a circle
+
+theta= 117*(%pi/180) //angle in radian
+r=3.5 //radius in m
+A=r*r*theta/2 //Area of sector
+printf('Area of sector = %.2f m^2',A)
diff --git a/2915/CH5/EX5.1/5_1.JPG b/2915/CH5/EX5.1/5_1.JPG Binary files differnew file mode 100755 index 000000000..c3bd9d128 --- /dev/null +++ b/2915/CH5/EX5.1/5_1.JPG diff --git a/2915/CH5/EX5.1/Ex5_1.sce b/2915/CH5/EX5.1/Ex5_1.sce new file mode 100755 index 000000000..ab91e5e13 --- /dev/null +++ b/2915/CH5/EX5.1/Ex5_1.sce @@ -0,0 +1,11 @@ +//Example 5.1
+//To sketch the graph of minus sinx in a given interval
+clear,clc;
+
+x = linspace(-0,2*%pi,50);
+y = -sin(x) ;
+set(gca(),"grid",[5 5]);
+plot(x,y);
+xlabel("$0\le x\le 2*pi$","fontsize",4,"color","red");
+ylabel("$y(x)=-sin(x)$","fontsize",4,"color","red");
+title("Example 5.1","color","blue","fontsize",9);
diff --git a/2915/CH5/EX5.1/plot5_1.jpeg b/2915/CH5/EX5.1/plot5_1.jpeg Binary files differnew file mode 100755 index 000000000..0638cbf04 --- /dev/null +++ b/2915/CH5/EX5.1/plot5_1.jpeg diff --git a/2915/CH5/EX5.10/5_10.JPG b/2915/CH5/EX5.10/5_10.JPG Binary files differnew file mode 100755 index 000000000..0922665c0 --- /dev/null +++ b/2915/CH5/EX5.10/5_10.JPG diff --git a/2915/CH5/EX5.10/Ex5_10.sce b/2915/CH5/EX5.10/Ex5_10.sce new file mode 100755 index 000000000..0a13b2e8b --- /dev/null +++ b/2915/CH5/EX5.10/Ex5_10.sce @@ -0,0 +1,26 @@ +//Example 5.10
+//To find the period of given function
+clear,clc;
+
+x = linspace(-0,2*%pi,200);
+y1=cos(6*x); //1st part of given function
+multiple1=6;//multiplicity of angle
+period_cosx=2*%pi ;//period of cos(x) is 2 pi
+period1= period_cosx/ multiple1;
+printf('Note: Period of cos(%d*x)= %f radians\n',multiple1,period1);
+y2= sin(4*x); //second part of given function
+multiple2=4; //multiplicity of angle
+period_sinx=2*%pi ;//period of sin(x) is 2 pi
+period2= period_sinx/multiple2;
+printf('Period of sin(%d*x)= %f radians\n',multiple2,period2);
+
+locm = %pi ;//LCM of period1 and period 2
+period = locm ;//final period
+printf('\nRequired period is %f radians',period);
+x = linspace(0,2*%pi,200);
+y = cos(6*x)+ sin(4*x);//given function
+set(gca(),"grid",[5 5]);
+plot(x,y,'r');
+xlabel("$0\le x\le 2*pi$","fontsize",4,"color","red");
+ylabel("$y(x)= sin(4*x) +cos(6*x)$","fontsize",4,"color","red");
+title("Example 5.10","color","red","fontsize",9);
diff --git a/2915/CH5/EX5.10/plot5_10.jpeg b/2915/CH5/EX5.10/plot5_10.jpeg Binary files differnew file mode 100755 index 000000000..0af99cf79 --- /dev/null +++ b/2915/CH5/EX5.10/plot5_10.jpeg diff --git a/2915/CH5/EX5.11/5_11.JPG b/2915/CH5/EX5.11/5_11.JPG Binary files differnew file mode 100755 index 000000000..bd88bc355 --- /dev/null +++ b/2915/CH5/EX5.11/5_11.JPG diff --git a/2915/CH5/EX5.11/Ex5_11.sce b/2915/CH5/EX5.11/Ex5_11.sce new file mode 100755 index 000000000..e492dc1c3 --- /dev/null +++ b/2915/CH5/EX5.11/Ex5_11.sce @@ -0,0 +1,23 @@ +//Example 5.11
+//To find the amplitude phase shift and period of given function
+clear,clc;
+
+x = linspace(-0,2*%pi,200);
+deviation = %pi; //deviation from multiples of x
+y = 3*cos(2*x- deviation) ;//given function
+amplitude = y/ cos(2*x- %pi) ;
+printf('Amplitude = %f\n',amplitude);
+multiple = 2; //multiplicity of angle
+period_cosx = 2*%pi; //period of sin(x) in radians
+required_period = period_cosx / multiple;
+printf('Required period = %f radians\n',required_period);
+phase_shift = deviation / multiple;
+printf('Phase shift = %f radians',phase_shift);
+
+x = linspace(-0,2*%pi,200);
+y = 3*cos(2*x- %pi) ;
+set(gca(),"grid",[5 5]);
+plot(x,y);
+xlabel("$0\le x\le 2*pi$","fontsize",4,"color","red");
+ylabel("$y(x)=3*cos(2*x- pi)$","fontsize",4,"color","red");
+title("Example 5.11","color","blue","fontsize",9);
diff --git a/2915/CH5/EX5.11/plot5_11.jpeg b/2915/CH5/EX5.11/plot5_11.jpeg Binary files differnew file mode 100755 index 000000000..2286dfc1a --- /dev/null +++ b/2915/CH5/EX5.11/plot5_11.jpeg diff --git a/2915/CH5/EX5.12/5_12.JPG b/2915/CH5/EX5.12/5_12.JPG Binary files differnew file mode 100755 index 000000000..39d734c77 --- /dev/null +++ b/2915/CH5/EX5.12/5_12.JPG diff --git a/2915/CH5/EX5.12/Ex5_12.sce b/2915/CH5/EX5.12/Ex5_12.sce new file mode 100755 index 000000000..d4bd2b8f6 --- /dev/null +++ b/2915/CH5/EX5.12/Ex5_12.sce @@ -0,0 +1,22 @@ +//Example 5.12
+//To find the amplitude phase shift and period of given function
+clear,clc;
+
+x = linspace(-%pi/6,4*%pi/3,200);
+deviation = -%pi/2;//deviation from multiples of x
+y = -2*sin(3*x- deviation) ;// given function
+amplitude = abs(y/(sin(3*x- deviation)) );
+printf('Amplitude = %f\n',amplitude);
+multiple = 3; //multiplicity of angle
+period_sinx = 2*%pi ;//period of sin(x) in radians
+required_period = period_sinx / multiple;
+printf('Required period = %f radians\n',required_period);
+phase_shift = deviation / multiple;
+printf('Phase shift = %f radians',phase_shift);
+
+x = linspace(-%pi/6,4*%pi/3,200);
+y =-2*sin(3*x+ %pi/2) ;
+set(gca(),"grid",[5 5]);
+plot(x,y);
+ylabel("$y =-2*sin(3*x+ %pi/2)$","fontsize",4,"color","red");
+title("Example 5.12","color","blue","fontsize",9);
diff --git a/2915/CH5/EX5.12/plot5_12.jpeg b/2915/CH5/EX5.12/plot5_12.jpeg Binary files differnew file mode 100755 index 000000000..0228906b8 --- /dev/null +++ b/2915/CH5/EX5.12/plot5_12.jpeg diff --git a/2915/CH5/EX5.13/Ex5_13.sce b/2915/CH5/EX5.13/Ex5_13.sce new file mode 100755 index 000000000..cf58cfde8 --- /dev/null +++ b/2915/CH5/EX5.13/Ex5_13.sce @@ -0,0 +1,9 @@ +clc,clear;
+//Example 5.13
+//To determine inverse sine function of a given value
+
+given = sin(%pi/4); //given value
+answer= asin(given); //final answer
+
+printf('Required answer is %f radians',answer);
+printf('\n\nOR \n\n(pi/4)*%f radians',answer*(4/%pi));
diff --git a/2915/CH5/EX5.14/Ex5_14.sce b/2915/CH5/EX5.14/Ex5_14.sce new file mode 100755 index 000000000..6970e36fe --- /dev/null +++ b/2915/CH5/EX5.14/Ex5_14.sce @@ -0,0 +1,9 @@ +clc,clear;
+//Example 5.14
+//To determine inverse sine function of a given value
+
+given = sin(5*%pi/4); //given value
+answer= asin(given); //final answer
+
+printf('Required answer is %f radians',answer);
+printf('\n\nOR \n\n(pi/4)*%f radians',answer*(4/%pi));
diff --git a/2915/CH5/EX5.15/Ex5_15.sce b/2915/CH5/EX5.15/Ex5_15.sce new file mode 100755 index 000000000..e68af7d27 --- /dev/null +++ b/2915/CH5/EX5.15/Ex5_15.sce @@ -0,0 +1,9 @@ +clc,clear;
+//Example 5.15
+//To determine inverse cosine function of a given value
+
+given = cos(%pi/3); //given value
+answer= acos(given); //final answer
+
+printf('Required answer is %f radians',answer);
+printf('\n\nOR \n\n(pi/3)*%f radians',answer*(3/%pi));
diff --git a/2915/CH5/EX5.16/Ex5_16.sce b/2915/CH5/EX5.16/Ex5_16.sce new file mode 100755 index 000000000..d94f4255c --- /dev/null +++ b/2915/CH5/EX5.16/Ex5_16.sce @@ -0,0 +1,9 @@ +clc,clear;
+//Example 5.16
+//To determine inverse cosine function of a given value
+
+given = cos(4*%pi/3); //given value
+answer= acos(given); //final answer
+
+printf('Required answer is %f radians',answer);
+printf('\n\nOR \n\n(pi/3)*%f radians',answer*(3/%pi));
diff --git a/2915/CH5/EX5.17/Ex5_17.sce b/2915/CH5/EX5.17/Ex5_17.sce new file mode 100755 index 000000000..7e76e85aa --- /dev/null +++ b/2915/CH5/EX5.17/Ex5_17.sce @@ -0,0 +1,9 @@ +clc,clear;
+//Example 5.17
+//To determine inverse tan function of a given value
+
+given = tan(%pi/4); //given value
+answer= atan(given); //final answer
+
+printf('Required answer is %f radians',answer);
+printf('\n\nOR \n\n(pi/4)*%f radians',answer*(4/%pi));
diff --git a/2915/CH5/EX5.18/Ex5_18.sce b/2915/CH5/EX5.18/Ex5_18.sce new file mode 100755 index 000000000..b61a788ef --- /dev/null +++ b/2915/CH5/EX5.18/Ex5_18.sce @@ -0,0 +1,8 @@ +clc,clear;
+//Example 5.18
+//To determine inverse tan function of a given value
+
+given = tan(%pi); //given value
+answer= atan(given);//final answer
+
+printf('Required answer is %f radians',answer);
diff --git a/2915/CH5/EX5.19/Ex5_19.sce b/2915/CH5/EX5.19/Ex5_19.sce new file mode 100755 index 000000000..f04f036be --- /dev/null +++ b/2915/CH5/EX5.19/Ex5_19.sce @@ -0,0 +1,7 @@ +clc,clear;
+//Example 5.19
+//To determine exact value of given expression involving inverse trigonometric functions
+
+expression= cos(asin(-1/4)); //given expresion
+
+printf('Value of given expression is %f radians',expression);
diff --git a/2915/CH5/EX5.2/5_2.JPG b/2915/CH5/EX5.2/5_2.JPG Binary files differnew file mode 100755 index 000000000..3ead4670c --- /dev/null +++ b/2915/CH5/EX5.2/5_2.JPG diff --git a/2915/CH5/EX5.2/Ex5_2.sce b/2915/CH5/EX5.2/Ex5_2.sce new file mode 100755 index 000000000..cedf11a15 --- /dev/null +++ b/2915/CH5/EX5.2/Ex5_2.sce @@ -0,0 +1,11 @@ +//Example 5.2
+//To sketch the graph of function of 1+cos(x) in given interval
+clear,clc;
+
+x = linspace(-0,2*%pi,50);
+y = 1+cos(x) ;
+set(gca(),"grid",[5 5]);
+plot(x,y);
+xlabel("$0\le x\le 2*pi$","fontsize",4,"color","red");
+ylabel("$y(x)=1+cos(x)$","fontsize",4,"color","red");
+title("Example 5.2","color","blue","fontsize",9);
diff --git a/2915/CH5/EX5.2/plot5_2.jpeg b/2915/CH5/EX5.2/plot5_2.jpeg Binary files differnew file mode 100755 index 000000000..a2fae9c25 --- /dev/null +++ b/2915/CH5/EX5.2/plot5_2.jpeg diff --git a/2915/CH5/EX5.4/5_4.JPG b/2915/CH5/EX5.4/5_4.JPG Binary files differnew file mode 100755 index 000000000..f521ee2c6 --- /dev/null +++ b/2915/CH5/EX5.4/5_4.JPG diff --git a/2915/CH5/EX5.4/Ex5_4.sce b/2915/CH5/EX5.4/Ex5_4.sce new file mode 100755 index 000000000..1dd111e4f --- /dev/null +++ b/2915/CH5/EX5.4/Ex5_4.sce @@ -0,0 +1,23 @@ +//Example 5.4
+//To determine the period of given sinusoidal function
+clear,clc;
+
+multiple = 2; //multiplicity of angle
+period_sinx = 2*%pi ;//period of sin(x) in radians
+required_period = period_sinx / multiple;
+printf('Required period is %f radians',required_period);
+
+//Note that sin 2x “goes twice as fast” as sin x.
+//While sin x takes a full 2*pi radians to go through an entire cycle
+//sin 2x goes through an entire cycle in just pi radians
+
+x = linspace(-0,2*%pi,100);
+y = sin(2*x) ;
+z = sin(x) ;
+set(gca(),"grid",[4 4]);
+plot(x,y,'r-');
+plot(x,z,'b-');
+xlabel("$0\le x\le 2*pi$","fontsize",4,"color","red");
+ylabel("$y(x)=sin(2x)$","fontsize",4,"color","red");
+title("Example 5.4","color","blue","fontsize",9);
+legend(["sin(2x)";"sin(x)"]);
diff --git a/2915/CH5/EX5.4/plot5_4.jpeg b/2915/CH5/EX5.4/plot5_4.jpeg Binary files differnew file mode 100755 index 000000000..ccc247e58 --- /dev/null +++ b/2915/CH5/EX5.4/plot5_4.jpeg diff --git a/2915/CH5/EX5.5/5_5.JPG b/2915/CH5/EX5.5/5_5.JPG Binary files differnew file mode 100755 index 000000000..f60d997dc --- /dev/null +++ b/2915/CH5/EX5.5/5_5.JPG diff --git a/2915/CH5/EX5.5/Ex5_5.sce b/2915/CH5/EX5.5/Ex5_5.sce new file mode 100755 index 000000000..ee3773d06 --- /dev/null +++ b/2915/CH5/EX5.5/Ex5_5.sce @@ -0,0 +1,25 @@ +//Example 5.5
+//To determine the period of 2 given cosine functions
+clear,clc;
+
+//y=cos(3*x)
+multiple = 3; //multiplicity of angle
+period_cosx = 2*%pi; //period of sin(x) in radians
+required_period = period_cosx / multiple;
+printf('Period of cos(3*x)is %f radians\n',required_period);
+
+//y=cos(0.5*x)
+multiple = 1/2; //multiplicity of angle
+period_cosx = 2*%pi; //period of sin(x) in radians
+required_period = period_cosx / multiple;
+printf('Period of cos(x/2)is %f radians',required_period);
+
+x = linspace(-0,4*%pi,200);
+y = cos(3*x) ;
+z = cos(x/2) ;
+set(gca(),"grid",[4 4]);
+plot(x,y,'r-');
+plot(x,z,'b-');
+xlabel("$0\le x\le 4*pi$","fontsize",4,"color","red");
+title("Example 5.5","color","blue","fontsize",9);
+legend(["y = cos(3x)";"y = cos(x/2)"]);
diff --git a/2915/CH5/EX5.5/plot5_5.jpeg b/2915/CH5/EX5.5/plot5_5.jpeg Binary files differnew file mode 100755 index 000000000..e142fca42 --- /dev/null +++ b/2915/CH5/EX5.5/plot5_5.jpeg diff --git a/2915/CH5/EX5.6/5_6.JPG b/2915/CH5/EX5.6/5_6.JPG Binary files differnew file mode 100755 index 000000000..b30335715 --- /dev/null +++ b/2915/CH5/EX5.6/5_6.JPG diff --git a/2915/CH5/EX5.6/Ex5_6.sce b/2915/CH5/EX5.6/Ex5_6.sce new file mode 100755 index 000000000..7961f10e2 --- /dev/null +++ b/2915/CH5/EX5.6/Ex5_6.sce @@ -0,0 +1,21 @@ +//Example 5.6
+//To determine the amplitude and period of given function
+clear,clc;
+
+x = linspace(-0,4*%pi,200);
+y = 3*cos(2*x) ; //given function
+amplitude = y/cos(2*x);
+printf('Amplitude = %f',amplitude);
+
+multiple = 2; //multiplicity of angle
+period_cosx=2*%pi; //period od cos(x)
+period_required = period_cosx / multiple;
+printf('\nPeriod = %f radians',period_required);
+
+x = linspace(-0,2*%pi,50);
+y = 3*cos(2*x) ;
+set(gca(),"grid",[5 5]);
+plot(x,y);
+xlabel("$0\le x\le 2*pi$","fontsize",4,"color","red");
+ylabel("$y(x)=3*cos(2*x)$","fontsize",4,"color","red");
+title("Example 5.6","color","blue","fontsize",9);
diff --git a/2915/CH5/EX5.6/plot5_6.jpeg b/2915/CH5/EX5.6/plot5_6.jpeg Binary files differnew file mode 100755 index 000000000..9ae8208a8 --- /dev/null +++ b/2915/CH5/EX5.6/plot5_6.jpeg diff --git a/2915/CH5/EX5.7/5_7.JPG b/2915/CH5/EX5.7/5_7.JPG Binary files differnew file mode 100755 index 000000000..d9c375fc0 --- /dev/null +++ b/2915/CH5/EX5.7/5_7.JPG diff --git a/2915/CH5/EX5.7/Ex5_7.sce b/2915/CH5/EX5.7/Ex5_7.sce new file mode 100755 index 000000000..23e70a4ea --- /dev/null +++ b/2915/CH5/EX5.7/Ex5_7.sce @@ -0,0 +1,28 @@ +//Example 5.7
+//To find amplitude and period of given composite function
+clear,clc;
+
+x = linspace(0,3,200);
+y1=2 ;//1st part of given function
+amplitude1=y1 ;//amplitude numerically same for constant function
+y2= -3*sin((2*%pi/3)*x); //second part of given function
+amplitude2 = abs(y2/sin((2*%pi/3)*x)) ;//amplitude of part 2
+//Note: adding 2 doesnt change ampitude
+//It just causes the upward shift of graph
+maax =amplitude1 + amplitude2; //altered maximum due to adding of 2
+minn =amplitude1 - amplitude2;//altered minimum due to adding of 2
+amplitude = (maax-minn)/2;//required amplitude
+printf('Amplitude = %f',amplitude);
+
+multiple=2*%pi/3 ;//multiplicity of angle
+period_sinx=2*%pi;//period of sin_x
+period_required = period_sinx/ multiple;
+printf('\nRequired period is %f radians',period_required);
+
+x = linspace(0,3,200);
+y = 2 -3*sin((2*%pi/3)*x)
+set(gca(),"grid",[5 5]);
+plot(x,y);
+xlabel("$0\le x\le 3$","fontsize",4,"color","red");
+ylabel("$y(x)= 2 -3*sin((2*%pi/3)*x)$","fontsize",4,"color","red");
+title("Example 5.7","color","blue","fontsize",9);
diff --git a/2915/CH5/EX5.7/plot5_7.jpeg b/2915/CH5/EX5.7/plot5_7.jpeg Binary files differnew file mode 100755 index 000000000..ebddb95de --- /dev/null +++ b/2915/CH5/EX5.7/plot5_7.jpeg diff --git a/2915/CH5/EX5.8/5_8.JPG b/2915/CH5/EX5.8/5_8.JPG Binary files differnew file mode 100755 index 000000000..f71bf3b29 --- /dev/null +++ b/2915/CH5/EX5.8/5_8.JPG diff --git a/2915/CH5/EX5.8/Ex5_8.sce b/2915/CH5/EX5.8/Ex5_8.sce new file mode 100755 index 000000000..4751cc1dd --- /dev/null +++ b/2915/CH5/EX5.8/Ex5_8.sce @@ -0,0 +1,28 @@ +//Example 5.8
+//To find the amplitude and period of given function
+clear,clc;
+
+//Period
+printf('PERIOD:\n')
+printf('This isnt a periodic function as x^2 is linearly related to x \n')
+printf('and hence period doesnt exist\n')
+
+//Amplitude
+x = linspace(0,2*%pi,200);
+y = 2*sin(x^2);
+amplitude= y/sin(x^2);
+printf('AMPLITUDE:\n')
+printf('Amplitude exists unlike period\n')
+printf('Because sine component of the given function never exceeds 1\n')
+printf('Function value is always ;ess than constant factor adjacent to sine\n')
+printf('Hence amplitude is the constant factor multiplied with sine component\n\n')
+printf('Amplitude = %f as calculated\n',amplitude)
+
+
+x = linspace(0,2*%pi,200);
+y = 2*sin(x^2) ;
+set(gca(),"grid",[5 5]);
+plot(x,y,'b');
+xlabel("$0\le x\le 2*pi$","fontsize",4,"color","red");
+ylabel("$y(x)= 2*sin(x^2)$","fontsize",4,"color","red");
+title("Example 5.8","color","red","fontsize",9);
diff --git a/2915/CH5/EX5.8/plot5_8.jpeg b/2915/CH5/EX5.8/plot5_8.jpeg Binary files differnew file mode 100755 index 000000000..52a7dce08 --- /dev/null +++ b/2915/CH5/EX5.8/plot5_8.jpeg diff --git a/2915/CH5/EX5.9/5_9.JPG b/2915/CH5/EX5.9/5_9.JPG Binary files differnew file mode 100755 index 000000000..6320120aa --- /dev/null +++ b/2915/CH5/EX5.9/5_9.JPG diff --git a/2915/CH5/EX5.9/Ex5_9.sce b/2915/CH5/EX5.9/Ex5_9.sce new file mode 100755 index 000000000..85f449dc5 --- /dev/null +++ b/2915/CH5/EX5.9/Ex5_9.sce @@ -0,0 +1,31 @@ +//Example 5.9
+//To find the amplitude and period of given function
+clear,clc;
+
+//amplitude
+x = linspace(-0,4*%pi,200);
+y1=3*sin(x); //1st part of given function
+amplitude1=y1/sin(x); //amplitude of part 1
+y2= 4*cos(x); //second part of given function
+amplitude2 =y2/(cos(x)); //amplitude of part 2
+
+//given function is a composition of 2 functions
+//Using trigonometric identities, merge them into 1
+//the amplitude of resultant is the required amplitude
+//In this case the merged function can be sine or cos
+//merging sine and cos into sine,
+amplitude = sqrt(amplitude1^2 + amplitude2^2);
+printf('Amplitude = %f',amplitude);
+
+//period
+period_cosx=2*%pi ;//period of cos(x) is 2 pi
+period_sinx=2*%pi ;//period of sin(x) is 2 pi
+locm = 2*%pi; //lcm of period_sinx and period_cosx
+printf('\nRequired period is %f radians',locm);
+x = linspace(0,4*%pi,200);
+y = 3*sin(x) +4*cos(x);
+set(gca(),"grid",[5 5]);
+plot(x,y,'r');
+xlabel("$0\le x\le 4*pi$","fontsize",4,"color","red");
+ylabel("$y(x)= 3*sin(x) +4*cos(x)$","fontsize",4,"color","red");
+title("Example 5.9","color","red","fontsize",9);
diff --git a/2915/CH5/EX5.9/plot5_9.jpeg b/2915/CH5/EX5.9/plot5_9.jpeg Binary files differnew file mode 100755 index 000000000..b8b10e873 --- /dev/null +++ b/2915/CH5/EX5.9/plot5_9.jpeg diff --git a/2915/CH6/EX6.10/Ex6_10.sce b/2915/CH6/EX6.10/Ex6_10.sce new file mode 100755 index 000000000..65e4316b1 --- /dev/null +++ b/2915/CH6/EX6.10/Ex6_10.sce @@ -0,0 +1,14 @@ +clc,clear
+//Example 6.10
+//To represent given complex number in trigonometric form
+
+z=-2 + -1*%i ;//given number
+x=real(z) ;//real part
+y=imag(z) ;//imaginary part
+
+//theta is in third quadrant as x and y are -ve
+theta=180 + atand(y/x);
+r=sqrt(x^2+y^2) ;//modulus of z
+printf('z= %f + i* %f can be written as: \n',real(z),imag(z))
+printf('z = sqrt(%.0f)*(cos(%.1f)+i*sin(%.1f))',r^2,theta,theta)
+
diff --git a/2915/CH6/EX6.11/Ex6_11.sce b/2915/CH6/EX6.11/Ex6_11.sce new file mode 100755 index 000000000..146fc00a3 --- /dev/null +++ b/2915/CH6/EX6.11/Ex6_11.sce @@ -0,0 +1,22 @@ +clc,clear
+//Example 6.11
+//To determine product and ratio of complex numbers using formula
+
+//given values
+z1 = 6*(cosd(70)+ %i*sind(70));
+z2 = 2*(cosd(31)+ %i*sind(31));
+
+//arguements of complex numbers
+theta1=phasemag(z1);
+theta2=phasemag(z2);
+//modulus of complex numbers
+r1=abs(z1);
+r2=abs(z2);
+theta_1p2 =theta1 + theta2 ;//theta1 + theta 2
+theta_1m2 =theta1 - theta2 ;//theta1 - theta 2
+//according to the formula used in book
+product = r1*r2*(cosd(theta_1p2)+%i*sind(theta_1p2));
+ratio = (r1/r2)*(cosd(theta_1m2)+%i*sind(theta_1m2));
+
+printf('z1*z2 = %.0f*(cos(%.0f)+i*sin(%.0f))\n',r1*r2,phasemag(product),phasemag(product))
+printf('z1/z2 = %.0f*(cos(%.0f)+i*sin(%.0f))\n',r1/r2,phasemag(ratio),phasemag(ratio))
diff --git a/2915/CH6/EX6.12/Ex6_12.sce b/2915/CH6/EX6.12/Ex6_12.sce new file mode 100755 index 000000000..876856cfb --- /dev/null +++ b/2915/CH6/EX6.12/Ex6_12.sce @@ -0,0 +1,13 @@ +clc,clear
+//Example 6.12
+//To find higher powers of complex number using demoivre theorem
+
+z= complex(1,1);
+r= abs(z);//modulus of z
+theta=phasemag(z) ;//arguement of z
+power=10;
+//using demoivre formula
+answer= (r^power)*(cosd(theta*power)+%i*sind(theta*power));
+//printf('(1+i)^10 = (%.0f)*(cos(%.0f)+ i*sin(%.0f))',r^power,theta*power,theta*power);
+printf('\n %.0f + %.0f*i',real(answer),imag(answer));
+printf('\n(OR)\n %.0f*i',imag(answer));
diff --git a/2915/CH6/EX6.13/Ex6_13.sce b/2915/CH6/EX6.13/Ex6_13.sce new file mode 100755 index 000000000..09ab024c2 --- /dev/null +++ b/2915/CH6/EX6.13/Ex6_13.sce @@ -0,0 +1,22 @@ +clc,clear
+//Example 6.13
+//To determine the cube roots of i
+
+z=%i //given complex number
+//modulii for cuberoots
+r1=abs(z)^(1/3)
+r2=abs(z)^(1/3)
+r3=abs(z)^(1/3)
+
+//arguements for cuberoots
+theta1= (phasemag(z)+360*0)/3
+theta2= (phasemag(z)+360*1)/3
+theta3= (phasemag(z)+360*2)/3
+
+cube_root_1 = r1 *(cosd(theta1)+ %i*sind(theta1))
+cube_root_2 = r2 *(cosd(theta2)+ %i*sind(theta2))
+cube_root_3 = r3 *(cosd(theta3)+ %i*sind(theta3))
+
+printf('cuberoot 1: %f + %f*i\n',real(cube_root_1),imag(cube_root_1))
+printf('cuberoot 2: %f + %f*i\n',real(cube_root_2),imag(cube_root_2))
+printf('cuberoot 3: %f + %f*i\n',real(cube_root_3),imag(cube_root_3))
diff --git a/2915/CH6/EX6.15/Ex6_15.sce b/2915/CH6/EX6.15/Ex6_15.sce new file mode 100755 index 000000000..0fe744500 --- /dev/null +++ b/2915/CH6/EX6.15/Ex6_15.sce @@ -0,0 +1,24 @@ +clc,clear
+//Example 6.15
+//To convert from polar to cartesian coordinates
+
+//part(a)
+r=2 ;
+theta=30 ;
+x=r*cosd(theta) ;
+y=r*sind(theta) ;
+printf('(a)(x,y)= (%f,%f)\n',x,y) ;
+
+//part(b)
+r=3 ;
+theta=3*%pi/4 ;
+x=r*cos(theta) ;
+y=r*sin(theta) ;
+printf('(b)(x,y)= (%f,%f)\n',x,y) ;
+
+//part(c)
+r=-1 ;
+theta=5*%pi/3 ;
+x=r*cos(theta) ;
+y=r*sin(theta) ;
+printf('(c)(x,y)= (%f,%f)',x,y) ;
diff --git a/2915/CH6/EX6.16/Ex6_16.sce b/2915/CH6/EX6.16/Ex6_16.sce new file mode 100755 index 000000000..78ab025be --- /dev/null +++ b/2915/CH6/EX6.16/Ex6_16.sce @@ -0,0 +1,32 @@ +clc,clear
+//Example 6.16
+//To convert from cartesian to polar coordinates
+
+//part(a)
+x=3 ;
+y=4 ;
+
+//53.13 is in same quadrant as(3,4)
+r=sqrt(x^2+y^2) ;
+theta=atand(y/x) ;
+printf('PART A\n(r,theta)= %f,%f',r,theta) ;
+printf('\nOR\n') ;
+r=-sqrt(x^2+y^2) ;
+//tan theta is +ve in 3rd quadrant
+//so 180 + 53.33 is also a permissible value
+theta=180 + atand(y/x) ;
+printf('(r,theta)= %f,%f',r,theta) ;
+
+//part(b)
+x=-5 ;
+y=-5 ;
+
+//225 is in same quadrant as(-5,-5)
+//tan theta is +ve in 3rd quadrant
+r=sqrt(x^2+y^2) ;
+theta=180+ atand(y/x) ;
+printf('\n\nPART B\n(r,theta)= %f,%f',r,theta) ;
+printf('\nOR\n') ;
+r=-sqrt(x^2+y^2) ;
+theta= atand(y/x) ;
+printf('(r,theta)= %f,%f',r,theta) ;
diff --git a/2915/CH6/EX6.17/Ex6_17.sce b/2915/CH6/EX6.17/Ex6_17.sce new file mode 100755 index 000000000..a6c7aa5f8 --- /dev/null +++ b/2915/CH6/EX6.17/Ex6_17.sce @@ -0,0 +1,11 @@ +clc,clear
+//Example 6.17
+//to express an equation in polar coordinates
+
+RHS=9 ;
+//Note that LHS is basically an equation of circle
+//But at any instant , it is numberically same as 9
+LHS_numerically=RHS ;
+r=sqrt(LHS_numerically) ;
+
+printf('The equation in terms of polar coordinates is : r =%.0f',r)
diff --git a/2915/CH6/EX6.19/Ex6_19.sce b/2915/CH6/EX6.19/Ex6_19.sce new file mode 100755 index 000000000..32d451137 --- /dev/null +++ b/2915/CH6/EX6.19/Ex6_19.sce @@ -0,0 +1,11 @@ +clc,clear
+//Example 6.19
+//to express an equation in polar coordinates
+
+//Given equation is : y=x
+y_by_x =1; //ratio of y and x
+tan_theta = y_by_x;
+theta=atand(tan_theta); //azimuth angle
+
+printf('The given equation in polar coordinates is : theta = %.0f degree\n',theta)
+printf('\nNote: Polar form is same regardless of value of r ')
diff --git a/2915/CH6/EX6.3/Ex6_3.sce b/2915/CH6/EX6.3/Ex6_3.sce new file mode 100755 index 000000000..952bb7556 --- /dev/null +++ b/2915/CH6/EX6.3/Ex6_3.sce @@ -0,0 +1,9 @@ +clc,clear
+//Example 6.3
+//To solve the given equation
+
+sec_theta = 1/2
+cos_theta = 1 / sec_theta
+printf('cos(theta) = %f as calculated\n',cos_theta)
+printf('But value of cos function can never exceed unity\n')
+printf('Thus, NO SOLUTION exists')
diff --git a/2915/CH6/EX6.4/Ex6_4.sce b/2915/CH6/EX6.4/Ex6_4.sce new file mode 100755 index 000000000..79b55174d --- /dev/null +++ b/2915/CH6/EX6.4/Ex6_4.sce @@ -0,0 +1,23 @@ +clc,clear
+//Example 6.4
+//To solve the given equation
+
+//Given equation is cos_theta = tan_theta
+//simplyfying given equation, we get
+//(sin_theta)^2 + sin_theta - 1 = 0
+//Solve for sin_theta as follows
+p=[1 1 -1]
+sin_theta= roots(p)
+printf('Values of sin(theta) after simplifying and solving = %f and %f\n',sin_theta(1),sin_theta(2))
+printf('Eliminate %f as sin_theta cant be below -1',sin_theta(1))
+
+//Since sin_theta is +ve, 2 solutions exist. in 1st and 2nd quadrant
+theta_1=asin(sin_theta(2)); //in 1st quadrant
+theta_2=%pi-asin(sin_theta(2));//the reflection in 2nd quadrant
+
+printf('\n\nSOLUTIONS:\n')
+printf('%f radians\n%f radians',theta_1,theta_2)
+
+printf('\n\nGENERAL SOLUTIONS:\n')
+printf('%f + integer multiples of 2pi \n',theta_1)
+printf('%f + integer multiples of 2pi \n',theta_2)
diff --git a/2915/CH6/EX6.9/Ex6_9.sce b/2915/CH6/EX6.9/Ex6_9.sce new file mode 100755 index 000000000..5e6306d2d --- /dev/null +++ b/2915/CH6/EX6.9/Ex6_9.sce @@ -0,0 +1,20 @@ +clc,clear
+//Example 6.9
+//To find the result of basic operations on 2 given complex numbers
+
+z1 = complex(-2,3)
+z2 = complex(3,4)
+
+summ = z1+z2
+difference = z1-z2
+product = z1*z2
+ratio = z1/z2
+mag_z1= abs(z1) //modulus of z1
+mag_z2= abs(z2)//modulus of z2
+//printf('Note: Please go through complex nos scilab syntaxes to comprehend this example code\n\n')
+printf('z1 + z2 = %.0f + %.0f*i\n',real(summ),imag(summ))
+printf('z1 - z2 = %.0f + %.0f*i\n',real(difference),imag(difference))
+printf('z1 * z2 = %.0f + %.0f*i\n',real(product),imag(product))
+printf('z1 / z2 = %f + %f*i\n',real(ratio),imag(ratio))
+printf('|z1|= sqrt(%.0f)= %f \n',mag_z1^2,mag_z1)
+printf('|z2| = %.0f',mag_z2)
diff --git a/2915/CH8/EX8.1/8_1.JPG b/2915/CH8/EX8.1/8_1.JPG Binary files differnew file mode 100755 index 000000000..afd8761a1 --- /dev/null +++ b/2915/CH8/EX8.1/8_1.JPG diff --git a/2915/CH8/EX8.1/Ex8_1.sce b/2915/CH8/EX8.1/Ex8_1.sce new file mode 100755 index 000000000..a54ad78e9 --- /dev/null +++ b/2915/CH8/EX8.1/Ex8_1.sce @@ -0,0 +1,16 @@ +//Example 8.1
+//To plot the function of sin(x)
+clear,clc;
+
+x = linspace(-0,2*%pi,50);
+y = sin(x) ;
+
+//For grid, uncomment below line
+//set(gca(),"grid",[5 5]);
+
+printf('NOTE:\nTo enable the grid , check the code')
+plot(x,y,'r');
+xlabel("$0\le x\le 2*pi$","fontsize",4,"color","red");
+ylabel("$y(x)=sin(x)$","fontsize",4,"color","red");
+title("Example 8.1","color","blue","fontsize",9);
+legend("sin(x)");
diff --git a/2915/CH8/EX8.1/plot8_1.jpeg b/2915/CH8/EX8.1/plot8_1.jpeg Binary files differnew file mode 100755 index 000000000..b5c5fd5cd --- /dev/null +++ b/2915/CH8/EX8.1/plot8_1.jpeg |
