Question

Which equation can be used to determine the reference angle, r, if theta=7pi/12?

Answer 1

r = 180° -
`(7\pi )/(12)`

Explanation:

We have to find the reference angle (r) of the given angle θ =
`(7\pi )/(12)`

First we will find the quadrant in which this angle lies.

Since θ =
`(7\pi )/(12)` =
`(7*180)/(12) = 105`

105° angle lies in second quadrant. Therefore, reference angle will be

r = 180° - θ

where θ =
`(7\pi )/(12)`

Now we can say that equation for reference angle r will be r = 180°-
`(7\pi )/(12)`

Answer 2

The reference angle will be
r = min(7π/12, π -7π/12) = 5π/12