# Video: Finding Principal Angles

Given the angle (273π)/3, find the principal angle.

02:10

### Video Transcript

Given the angle 273π over three, find the principal angle.

First of all, what is the principal angle? If we have a coordinate plane and the initial arm of the angle is at zero degrees and then we have a terminal arm somewhere. The counterclockwise angle between the initial arm and the terminal arm is a principal angle if it is between zero and 360 degrees or between zero and two π radians.

Weβve been given the angle that measures 273π over three. The first thing we can do is go ahead and divide 273 by three. When we do that, we find out that this angle is 91π. We can tell by this measure that weβre going to be working in radians and not degrees. 91π is larger than two π, which means itβs not a principal angle as it stands. We want to find out where would 91π fall on a coordinate system. If we let its initial arm be at zero and then if the terminal arm was also at zero after one turn, it would be two π.

But we can also say that four π would be located here, as would six π. At this point, we can think about 91π in a different way. 91π is the same thing as 90π plus one π. And 90π would be a terminal arm located along the π₯-axis. And if 90π is located here, then 91π would be located here. And if this is our angle π, to write 91π as a principal angle would be π.