What is/ how do I find the least positive coterminal arc and the reference arc of -10pi/3?

1 Answer
namralos
Jun 24, 2017

First add multiples of #2pi#.

Explanation:

Since #-(10pi)/3# is negative, we add #2pi# repeatedly until the angle becomes positive.

#-(10pi)/3 + 2pi = -(10pi)/3 + 6pi/3 = -(4pi)/3#
This is still negative. Add another #2pi#.

#-(4pi)/3 + 2pi = -(4pi)/3 + 6pi/3 = (2pi)/3#

The coterminal angle is #(2pi)/3#.

[ASIDE: If you had noticed that #2pi# was not sufficient, you could have added #4pi# to begin with -- instead of adding #2pi# twice.]

For every angle that is an integer multiple of #pi/3# in reduced form, the reference angle in Quadrant I is #pi/3#.

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