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

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.