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

Jul 25, 2018

$106 ' 16 '$ is $\theta$

#### Explanation:

First up, I would find what $\theta$ was if it is $\cos \theta = \frac{7}{25}$

$\cos \theta = \frac{7}{25}$
$\theta = {\cos}^{- 1} \left(\frac{7}{25}\right)$
$\theta = 73 ' 44 '$
This is know as the "reference angle"

Now since $\cos \theta$ 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 $180 - 73 ' 44 ' = 106 ' 16 '$