Given the information below, how do you write the code according to the terms be

Question

Given the information below, how do you write the code according to the terms below? The values for sin(x) and cos(x), where x is the angle in radians, can be approximated using the appropriate series shown below. The more terms you include in the series the more accurate your answers should be. sin(x) = x middot Product_n=1^infinity (1-x^2/n^2 pi^2) = x middot (1-x^2/1^2 pi^2)(1 - x^2/2^2 pi^2)(1 - x^2/2^2 pi^2)(1 - x^2/3^2 pi^2).... cos(x) = Product_n=1^infinity (1-4x^2/(2n-1)^2 pi^2) = (1-4x^2/1^2pi^2)(1-4X^2/3^2 pi^2)(1-4x^2/5^2 pi^2)...

Explanation / Answer

clc;
clear all;
close all;
format long
n=input('Enter the Angle in degree ');
x=n*pi/180; %%%% conversion in radians
fprintf('The Angle = %f degree',n);
fprintf(' ');
fprintf('The Angle = %f radians',x);
fprintf(' ');
%%%% for sin series %%%%%
sum=x;
for j=1:300
sum=sum*(1-x^2/(j^2*pi^2));
end
act_=sin(x);
fprintf('The sin x according to series after 300 iteration is = %f',sum);
fprintf(' ');
fprintf('The sin x according to intrinsic function is = %f',act_);
fprintf(' ');
% % % % cos x series %%%%
c_sum(1,1)=0;
c_sum(1,2)=1;
k=1;
while ( abs(c_sum(1,1)-c_sum(1,2)) > 0.000001)
c_sum(1,1)=c_sum(1,2);
c_sum(1,2)=c_sum(1,2)*(1-4*x^2/((2*k-1)^2*pi^2));
k=k+1;
end
act_=cos(x);
fprintf('The cos x according to series after %d iteration is = %f',k, c_sum(1,2));
fprintf(' ');
fprintf('The cos x according to intrinsic function is = %f',act_);
fprintf(' ');

Output:

Enter the Angle in degree 30
The Angle = 30.000000 degree
The Angle = 0.523599 radians
The sin x according to series after 300 iteration is = 0.500046
The sin x according to intrinsic function is = 0.500000
The cos x according to series after 157 iteration is = 0.866180
The cos x according to intrinsic function is = 0.866025

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