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objective-cfloating-pointios4trigonometry

Value of sine 180 is coming out as 1.22465e-16

I want to implement a Sine and Cosine calculator in ios4:

if([operation isEqual:@"sin"]){
    operand = (operand*M_PI/180.0);
    operand=sin(operand);
}

The code gives me correct answer for values from 0 through 90.

When I give value of 180, I get 1.22465e-16 as an answer. I expect zero.

Where does this small difference come from?

Solution

  • This is caused by the inability of a binary number system to exactly represent PI.

    One possible solution would be to use the symmetry of sin:

    sindeg(x) = sindeg(180 - x)

    (or alternatively):

    sin(x) = sin(M_PI - x)

    Transforming the angle into the range (-pi/2 : pi/2) reduces the error of the approximation.

    Basically:

    if([operation isEqual:@"sin"]){
  operand = fmod(operand, 360);
  if (operand > 270) operand -= 360;
  else if (operand > 90) operand = 180 - operand;
  operand=sin(operand*M_PI/180.0);
}