initial commit / add all books

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+//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);

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