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

1 Answer
Lucy
Jul 25, 2018

#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'#

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