Question

What does `sin(arc cos(2))+3cos(arctan(-1))` equal?

Answer 1

Nothing.

Explanation:

`arccos` is a function that is only defined on `[-1,1]` so `arccos(2)` doesn't exist.

On the other hand, `arctan` is defined on `RR` so `arctan(-1)` exists. It is an odd function so `arctan(-1) = -arctan(1) = -pi/4`.

So `3cos(arctan(-1)) = 3cos(-pi/4) = 3cos(pi/4) = (3sqrt(2))/2`.