Which quadrant does the terminal side of -509 degrees lie?

1 Answer



We have an angle of #-509^o#. Where is the terminal side?

First, the negative sign tells us we're moving in a clockwise direction, so from the positive x-axis, down into Q4 and around through Q3, Q2, Q1 and back to the x-axis again. We've gone #360^o# so let's subtract that off and see how far we have left to go:


Ok, so now let's move another 90 and sweep through Q4:


We can't move another full 90, so we end in Q3.