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

1 Answer

Q3

Explanation:

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:

509-360=149

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

149-90=59

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