Question

How do you find the exact value of `sec(theta) = -1`?

Answer 1

`theta=pi +2k pi` for `k in ZZ`

Explanation:

If you remember some foundamental values for cosine, you can also avoid tables and work with the definition of the secant function, which is

`sec(theta):=1/cos(theta)`

Then the equation `sec(theta)=-1` turns to `1/cos(theta)=-1`, which is equivalent to `cos(theta)=-1`. The only values of `theta` that satisfy this are `theta=pi +2k pi` for `k in ZZ`. If you prefer the notation with degrees: `theta=180°+360°k` for `k in ZZ`.