Question

How do you evaluate `csc^-1(-1)` without a calculator?

Answer 1

`csc^-1 (-1)=-pi/2`.

Explanation:

Recall the Defn. of `csc^-1` function :

`csc^-1 x=theta, |x| ge 1 iff csc theta=x, theta in [-pi/2,pi/2]-{0}`.

We have, `csc(-pi/2)=-1", where, "-pi/2 in [-pi/2,pi/2]-{0}, csc^-1 (-1)=-pi/2`.