Question

The value of cos(x) is evaluated as follows: cos⁡(x)=1- x^2/2!+ x^4/4!- x^6/6!+ x^8/8!+⋯+ x^2n/((2n)!) Where n is related to the accuracy level required for cos(x). Write a C++ program that asks the user to input n and x and then the program will evaluate cos(x) up to the 2n terms.

Answer 1

Solution:

#include<iostream>

#include<math.h>

using namespace std;

//method to calculate factorial

unsigned long long fact(unsigned long long n)

{

if(n==1)return 1;

return n*fact(n-1);

}

//method to compute cos(x)

double cos(unsigned long long n,double x)

{

double sum=1;

unsigned long i=2;

while(i<=(2*n))

{

double nume=pow(x,i);

unsigned long long d = fact(i);

//cout<<d<<endl;

//finding term value

nume = nume/d;

if(i%2==0)

{

sum=sum-nume;

}

else

{

sum=sum+nume;

}

i=i+2;

}

//returning sum

return sum;

}

int main()

{

//testing method

//reading input

unsigned long long n;

double x;

cout<<"Enter n and x:";

cin>>n>>x;

//displaying output

cout<<"cos("<<x<<") = "<<cos(n,x)<<endl;

return 0;

}