Question #b649e

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Answer 1 · 2018-01-25T04:21:05

#costheta=12/13#

Well, we can use the Pythagorean identity, which states that

#sin^2theta+cos^2theta=1#

We have: #sintheta=5/13#, #:.sin^2theta=25/169#

Putting that into the identity yields

#25/169+cos^2theta=1#

#cos^2theta=1-25/169#

#cos^2theta=144/169#

Square root both sides to get:

#costheta=+-12/13#

The equation #theta+alpha=90^@# indicates that #theta# is in the first quadrant, therefore, the positive value is the correct answer:

#costheta=12/13#