Approximate values for sine and cosine of an angle, x (radians), can be obtained

Question

Approximate values for sine and cosine of an angle, x (radians), can be obtained from the tollowing infinite series equations: sin x = x--+ + Eq. 1 5! cosx = 1--+ + Eq. 2 2 4 6! 1. Develop a procedure for iteratively determining values for sine and cosine using this relationship. Based on your algorithm, program a simultaneous solution to each equation in C or C++ to determine "sin x" and "cos x", then solve the Pythagorean Identity, sin x2 cos x2-1 , using your approximate values, for a given value ofx that is input by the user. Implement and run your program on the ULTRAVIOLET supercomputer. The results should display to screen in a tabular format. Include the % error obtained for the true value of 1.00000" 2.

Explanation / Answer

Here is the solution, do give me a thumbs up if this helps!

#include <iostream>

#include<math.h>

using namespace std;

double fact(int x)

{

int j=1;

if(x==0 || x==1)

return 1;

else

{

for(int i=2;i<=x;i++)

j*=i;

}

return j;

}

int main() {

double sinx=0, cosx=0,x;

cin>>x;

int i;

for(i=0;i<10000;i++)

{

sinx+=pow(-1,i)*pow(x,2*i+1)/fact(2*i+1);

cosx+=pow(-1,i)*pow(x,2*i)/fact(2*i);

}

cout<<sinx<<endl<<cosx;

cout<<pow(sinx,2)+pow(cosx,2);

return 0;

}

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