Why does -45 degrees equal 315 in trigonometry?

Question

Can someone explain that and how you get this: What are the values of θ, between 0 and 2pi, when tan θ=-1 ?

thanks

Answer 1

Think about it like you're looking at a clock face...

0° is at the 3 o'clock position and positive degrees are when you move counter clockwise. So 90° is at the 12 o'clock position.

If you were to move - 270° from 0°, that's saying you're moving 270° clockwise, which would still get you at the 12 o'clock position. So -270° = 90° in that you'll end up in the same location (12 o'clock)

So moving 45° clockwise (-45°) is the same as moving 315° counter clockwise. You'll end up at the same position on the unit circle.

For your second question:

tan θ = -1 in the second and fourth quadrant of the unit circle. In radians, this would be when θ = ^3π/₄ and when θ = ^7π/₄

Shoot me a message if this doesn't make sense I'll try to explain it better