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

// Pre-processor Directives
#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;
/* formula
x = 1 - pow(angle, 2)/factorial(2) + pow(angle, 4)/factorial(4) -
pow(angle, 6)/factorial(6) + pow(angle, 8)/factorial(8);*/
// For Loop
for (i=2; i<=8; i+=2)
{
if (i==4 || i==8)
{
x = x + pow(angle, i)/factorial(i);
}
else
{
x = x - pow(angle, i)/factorial(i);
}
}
return 1+x;
}
long factorial(long n)
{
if (n <= 1)
{
return 1;
}
else
{
return (n * factorial(n-1));
}
}

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