Math.cos inaccurancy

Question

alert(Math.cos(Math.PI/2));

Why the result is not exact zero? Is this inaccurancy, or some implementation error?

Answer 1

Math.PI/2 is an approximation of the real value of pi/2. Taking the exact cosine of this approximated value won't yield zero. The value you get is an approximation of this exact value up to the precision of the underlying floating point datatype.

Using some arbitrary precision library, you can evaluate the difference between pi/2 in double precision and the exact value to

 0.0000000000000000612323399573676588613032966137500529104874722961...

Since the slope of the cosine close to its zeros is 1, you would expect the cosine of the approximation of pi/2 to be approximately equal to this difference, and indeed it is.