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

1 Answer
NJ
Mar 18, 2018

#(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)#.

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