### 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.

Weβve 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 weβre going to be working in radians and not degrees. 91π is larger than two π, which means itβs 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.