Math.cos(Math.PI/2) returns 6.123031769111886e-17 in JavaScript & AS3?

Question

If I'm understanding this correct, both JavaScript and ActionScript 3 works with radians.

So the expected output of the following codes would be:

Math.PI                 //Expected 3.141592653589793, got 3.141592653589793

Math.sin(0)             //Expected 0, got 0
Math.sin(Math.PI/2)     //Expected 1, got 1
Math.sin(Math.PI)       //Expected 0, got 1.2246063538223773e-16
Math.sin(Math.PI*3/2)   //Expected -1, got -1
Math.sin(Math.PI*2)     //Expected 0, got -2.4492127076447545e-16

Math.cos(0)             //Expected 1, got 1
Math.cos(Math.PI/2)     //Expected 0, got 6.123031769111886e-17
Math.cos(Math.PI)       //Expected -1, got -1
Math.cos(Math.PI*3/2)   //Expected 0, got -1.836909530733566e-16
Math.cos(Math.PI*2)     //Expected 1, got 1

This is the same behavior in Firefox, Chrome, Safari and also in Flash Professional CS5.5. I'm using Mac OS X 10.7.2.

Test:

http://jsfiddle.net/KA4VM/

Answer 1

Have you looked at the value you're getting? You're expecting 0, but you're getting something like

0.00000000000000012246063538223773

Isn't that close enough to zero for you?

Basically, you shouldn't expect binary floating point operations to be exactly right when your inputs can't be expressed as exact binary values - which pi/2 can't, given that it's irrational. (You shouldn't expect the results to be exact even when the inputs can be expressed exactly in binary, if the output can't be expressed exactly...)