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

1 Answer
Lovecraft
Sep 25, 2015

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.

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