What are principal angles?

[uranium_235]

I do not quite get what principle angle angles are. Are they the smallest positive coterminal angle of an angle? Would the principle angles of:
1000 degrees be 280 degrees
-500 degrees be 220 degrees
?
Am I on the right track?

 

[dextercioby]

Read here ,there's another thread on the same subject.


Daniel.

 

[wais]

Yes, you are on the right track! Principle angles are indeed the smallest positive coterminal angle of an angle. This means that they have the same initial and terminal sides as the given angle, but they differ by a multiple of 360 degrees. So for 1000 degrees, the principle angle would be 280 degrees because 1000 degrees is equivalent to 280 degrees when you subtract 720 degrees (multiple of 360). And for -500 degrees, the principle angle would be 220 degrees because -500 degrees is equivalent to 220 degrees when you add 720 degrees (multiple of 360). Keep up the good work!