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Why use radians? For us, primarily, because C/C++ library functions such as sin(x), cos(x), etc. take angle in radians.
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The formula to calculate the circumference of a circle is 2*radius*PI
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One radian is equivalent to 180/PI degrees
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There are 2*PI radians in a circle
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/* radian, sin(), and cos() example */
#include <iostream>
#include <cmath>
using namespace std;
#define PI 3.14159265
int main ()
{
double degrees = 30.0;
double result = sin( degrees * PI / 180 );
cout << "The sine of "<< degrees << " degrees is "<< result << "\n";
result = cos( degrees * PI / 180 );
cout << "The cosine of "<< degrees << " degrees is "<< result << "\n";
// radians = (PI / 180) * degrees
// degrees = radians / (PI / 180) = radians * 180 / PI
cout << "One radian is "<< 180 / PI << " degrees\n";
return 0;
}
/*Output:
The sine of 30 degrees is 0.5
The cosine of 30 degrees is 0.866025
One radian is 57.2958 degrees
*/
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