Question

What is the reference angle in degrees for `(31pi)/6` ?

Answer 1

`(7pi)/6`

Explanation:

A circle is comprised of `360^o`. In order to find the reference angle, we need to reduce the current angle to an angle that is between `0^o` and `360^o`.

We start with `(31\pi)/6`.

We know that `0^o = (0pi)/6` and `360^o=2pi =(12pi)/6`

Since `360^o = 2pi` radians, we will subtract of `2pi=(12pi)/6` each iteration:

Iteration 1:
`(31pi)/6 - (12pi)/6 = (19pi)/6`

Iteration 2:
`(19pi)/6 - (12pi)/6 = (7pi)/6`

Since `0 \leq (7pi)/6 \leq (12pi)/6`, we can stop as we have found the reference angle.

The reference angle is `color(green)((7pi)/6)`.