Question

I need the answer to this question use pi and fractions

Answer 1

Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side.

In another words, are angles "located at the same place". We can find coterminal angles by adding or subtracting 2π from our angle.

First, let's add 2π.

`-(7\pi)/(4)+2\pi=-(7\pi)/(4)+(8\pi)/(4)=(-7\pi+8\pi)/(4)=(\pi)/(4)`

π/4 is a positive angle that is coterminal to -7π/4.

Now, let's subtract 2π.

`-(7\pi)/(4)-2\pi=-(7\pi)/(4)-(8\pi)/(4)=(-7\pi-8\pi)/(4)=-(15\pi)/(4)`

-15π/4 is a negative angle that is coterminal to -7π/4.