Thread: Calculating Sin/Cosine

  1. 09-11-2001 #1
    Josh
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    Question Calculating Sin/Cosine

    Hi,
    I'd like help getting started writing my own routines to calculate sin and cos. But I really don't know where to begin..

    This is what I know:

    sin(x) = x (for very small x)
    cos(x) = 1 (for very small x)
    sin(x) = 2*sin(x/2)*cos(x/2)
    cos(x) = (cos(x/2))^2 - (sin(x/2))^2 (where "^" means "power")

    This is what I've done so far:

    while (x >= 0.0001){ //first checks to see if x is really small
    mysinx == 2*(x div 2) * mycosx(x/2);
    }
    while(x = 1){
    mycos(x) == ((x/2))^2 - (mysinx(x/2))^2;
    }

    Thanks, Josh
  2. 09-11-2001 #2
    Salem
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    This looks like a recursive exercise

    There are two cases
    1. the limiting case - sin(x) = x (for very small x)
    2. the reducing case - sin(x) = 2*sin(x/2)*cos(x/2)

    Code:
    double sin ( double x ) {
    if ( x < 0.000001 ) {
        return x;  // case 1
    } else {
         return 2 * sin( x/2 ) * cos ( x/2 ); // case 2
    }
}
    Shrug....
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  3. 09-11-2001 #3
    SilentStrike
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    What about power series?

    That way, you could write one without relying on the other, and vice versa.

    Toward the bottom of the page..

    http://forum.swarthmore.edu/dr.math/....10.12.00.html
    Prove you can code in C++ or C# at TopCoder, referrer rrenaud
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