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

1 Answer
Jul 26, 2018

#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#°.