Question

What does `sin(arccos(6))-2csc(arcsec(9))` equal?

Answer 1

Undefined

Explanation:

The domain of the inverse of a function is the same as the range of the function. Then, as `arccos` is the inverse of cosine, the domain of `arccos` is equal to the range of `cos` which is `[-1, 1]`. As `6` lies outside that range, `arccos(6)` is undefined.

To see this without thinking about domain and range, just consider

`x = arccos(6)`

`=> cos(x) = cos(arccos(6)) = 6`

As `cos(x) in [-1, 1]` for all `x in RR` that means there is no such `x`, that is to say there is no value corresponding to `arccos(6)`