# What is the positive and negative angle that is coterminal with -150^\circ?

The closest ones are $- {150}^{\circ} + {360}^{\circ} = {210}^{\circ}$ and $- {150}^{\circ} - {360}^{\circ} = - {510}^{\circ}$ but there are plenty of others.
"Coterminal" -- I had to look it up. It's the word for two angles with the same trig functions. Coterminal presumably refers to something like the same spot on the unit circle. That means the angles differ by a multiple of ${360}^{\circ}$ or of $2 \pi$ radians.
So a positive angle coterminal with $- {150}^{\circ}$ would be $- {150}^{\circ} + {360}^{\circ} = {210}^{\circ} .$ We could have added ${1080}^{\circ} = 3 \times {360}^{\circ}$ and gotten ${930}^{\circ}$ which is also coterminal with $- {150}^{\circ} .$
Some negative angles coterminal with $- {150}^{\circ}$ are $- {150}^{\circ} - {360}^{\circ} = - {510}^{\circ}$ and $- {150}^{\circ} - {36000}^{\circ} = - {36150}^{\circ} .$