Why does Math.cos(90 * Math.PI/180) yield 6.123031769111... and not zero?

javascript math geometry trigonometry
Sean picture Sean · Mar 11, 2012 · Viewed 13.1k times · Source

I convert degrees to radians (degrees * Math.PI/180) but why does the following:

Math.cos(90 * Math.PI/180)

yield 6.123031769111... and not zero?

I'm trying to perform 2D rotations uses matrixes and the results are completely out of whack.

Answer

templatetypedef picture templatetypedef · Mar 11, 2012

The output of 

Math.cos(90 * Math.PI/180)

is

6.123031769111886e-17

Notice the e-17 at the end, which means that this number is 6.123 x 10-17. This is a number so vanishingly close to 0 that it's effectively 0. The reason that it's not identically 0 is due to rounding errors in the IEEE-754 double format which prevents you from getting an exact representation of π / 2 and causes minute rounding errors in the calculation of the cosine.

By the way - I was pretty surprised as well when the result came back starting with a 6! It's only after I looked at the very end that things started to make sense.

Hope this helps!

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