Question

How do you evaluate the expression `csc(-45)`?

Answer 1

`-sqrt2`

Explanation:

Recall that

`csctheta=1/sintheta` and `sin(-theta)=-sin(theta)`

With this in mind, we can rewrite our expression as

`1/sin(-45)`, which is the same as `1/-sin(45)`

The Unit Circle coordinates for `45^@` are `(sqrt2/2,sqrt2/2)` where the `y`-coordinate is the `sin` value. We now have

`1/-(sqrt2/2)`

Which can be rewritten as

`-2/sqrt2`, and rationalized as `-sqrt2`

Hope this helps!