Incorrrect evaluation of cos (90 deg)

[meadow-tulips]

Tried evaluating cos (90 deg) in the demo notepad.

Showing some weird value.
It should return 0

[josdejong]

This is the most asked question. It is a floating point round-off error.

See docs: https://mathjs.org/docs/datatypes/numbers.html#roundoff-errors

[nickkolok]

But how about a bunch of simplification rules? For angles of $15\cdot k$ degrees, representation with square roots always exists...

[josdejong]

It would be possible to implement checks for that, but since we're dealing with floating point numbers, such rounding-off logic will not work flawlessly and creates inconsistencies. For floating point calculations I think it is simply best to just accept the fact that there are round-off errors involved in general. The only real solution is to use symbolic computation, like extend math.simplify to replace sin(90 deg) and sin(2pi) with 0.

[lulunac27a]

It's because numbers in JavaScript uses 64-bit double precision numbers, so 90 degrees is pi/2 radians, since pi is an irrational number which cannot be expressed as a fraction and pi cannot be expressed in precise binary number as double precision numbers uses binary notation.