Question

How would I be able to figure out the reference angle in radians of `(5pi)/6`?

Answer 1

`pi/6`

Explanation:

The definition of the reference angle, is that it's the smallest angle that's made using the x-axis at reference while having the same coordinates at the unit circle.

`(5pi)/6` is an angle on the second quadrant, because `pi/2 < (5pi)/6 < pi`. So an angle in that quadrant has a representation, more or less like this:

Now, the angle in red is `(5pi)/6`, but you can see that the angle the blue line (the terminal side) makes with the axis is smaller. Since the sum of that angle (let's call it `theta`) and the angle in red must sum out to `pi` we have that:
`theta + (5pi)/6 = pi`
`theta = pi - (5pi)/6 = pi/6`

So that's your reference angle.