Question

How do you name an angle between `0^circ` and `360^circ` that is coterminal with the angle `-210^circ`?

Answer 1

`150`°

Explanation:

Angles that are coterminal with `-210`° can be written in the form:
`-210+360k` where `k` is some integer constant.

Using intuition, we pick out a value an integer for `k` that would result in a value that lies between `0`° and `360`°. In this case, `k` would be `1`, but if you don't have the intuition or you have time, you can just pick out several values for `k` that would make it lie around values between `0`° and `360`°.

Using `k=1`:
`-210 +360(1)` = `-210 + 360` = `150`°

or

Using several values for `k`:
we get ...`-930`°, `-570`°, `-210`°, `150`°, `510`°, `870`°...

All of these values are coterminal, but the only one that lies between `0`° and `360`° is `150`°.