The cosine of an angle can be computed from the following infinite series: cosx?

Question

The cosine of an angle can be computed from the following infinite series:

cosx?1?x2 ?x4 ?x6 ?........ 2! 4! 6!

Write a program that reads an angle x (in radians) from the keyboard. Then, in a function compute the cosine of the angle using first five terms of the series. Print the value computed along with the value of the cosine computed using the C++ library function.

3. The cosine of an angle can be computed from the following infinite series: cos x = 1--+ +. Q'.. Write a program that reads an angle x (in radians) from the keyboard. Then, in a function compute the cosine of the angle using first five terms of the series. Print the value computed along with the value of the cosine computed using the C++ library function.

Explanation / Answer

#include<iostream>
#include<cmath>
using namespace std;
double cosine(double angle);
long factorial(long n);
int main()
{
double angle;
cout << "Enter the angle in radians: ";
cin >> angle;
cout << "The calculated cosine of " << angle << " is " << cosine(angle) << endl;
cout << "The C++ cosine of " << angle << " is " << cos(angle) << endl;
system("PAUSE");
return 0;
}
double cosine(double angle)
{
double x=0;
double i;
double temp;
int count = 0;
x = 1 - pow(angle, 2)/factorial(2) + pow(angle, 4)/factorial(4) -pow(angle, 6)/factorial(6) + pow(angle, 8)/factorial(8);*/
for (i=2; i<=8; i+=2)
{
temp = pow(-1, i-1)*pow(angle, i)/factorial(i);
if (temp >.0001)
{
x = x + temp;
count++;
}
}
return 1+x;
}

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