Question

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

Answer 1

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.