write a c program Write two functions gx sinx and hx cosx

write a c++ program

Write two functions g(x) = sin(x) and h(x) = cos(x) using the series above to obtain accuracy to 5 decimal places. Write a C++ program that uses the functions above to calculate f(n) for integer n = 0, 1, 2, ..., 6, where f(n) = 5g(n) * h(4000 pi n + pi/3) = 5 sin(n) * cos(4000 pi n + pi/3)

Solution

#include <iostream>
using namespace std;

#define pi 3.14159265359
#define iter 5

double sin( double x ){
   double result = x;
   double last = x;
   for(int i = 1; i < iter; i++ ){
       last*= -1;
       last*= (x*x);
       last/= (2*i)*(2*i + 1);
       result += last;
   }
   return result;
}

double cos( double x ){
   double result = 1;
   double last = 1;
   for(int i = 1; i < iter; i++ ){
       last*= -1;
       last*= (x*x);
       last/= (2*i)*(2*i - 1);
       result += last;
   }
   return result;
}

double f( double x ){
   return 5*sin(x) + cos( 4000*pi*x + pi/3 );
}

int main(){
   cout << sin( pi/6 ) << endl;
   cout << cos( pi/3 ) << endl;
   cout << f( pi/6 ) << endl;
}