Question

How do you find two solutions of the equations `sectheta=-2`?

Answer 1

Two possible solutions are `theta=120^@` and `theta=240^@`

Explanation:

By definition `sec=("hypotenuse")/("adjacent side")`
for a triangle in standard position.

The `"hypotenuse"` is always taken to be positive,
so if `sec(theta)` is negative, the `"adjacent side"` must be on the negative X-axis.

The `abs("hypotenuse"):abs("adjacent side")` ratio of `2:1`
implies one of the common trigonometric reference angles, namely `60^@`

Since a straight line `=180^@`, the common solutions follow from the image below:

Adding multiples of `360^@` to either of these solutions, would give you further (but equivalent) solutions.