Question

If `costheta=-7/25`, and `90°<theta<180°` what is `theta`?

Answer 1

`106'16'` is `theta`

Explanation:

First up, I would find what `theta` was if it is `costheta=7/25`

`costheta=7/25`
`theta=cos^(-1)(7/25)`
`theta=73'44'`
This is know as the "reference angle"

![https://useruploads.socratic.org/mfnc6zElTkqPEE7Bu76T_reference_angle.jpg)

Now since `costheta` is negative in the second and third quadrant, then we can use the reference angle to find the angle in the second quadrant.

We go `180-73'44'=106'16'`