If $cos θ = - \frac{7}{25}$ $costheta=-7/25$ , and $90°<theta<180°$ what is $theta$ ?

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Answer 1 · 2018-07-25T02:25:51

$106'16'$ is $theta$

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 $180-73'44'=106'16'$

If costheta=-7/25cosθ=−725costheta=-7/25, and 90°<theta<180°90°<theta<180° what is thetatheta?