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

1 Answer
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.