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

1 Answer
Apr 27, 2018

The closest ones are -150^circ + 360^circ = 210^circ and -150^circ -360^circ = -510^circ but there are plenty of others.

Explanation:

"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 2pi 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.