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Bezzdna [24]
1 year ago
14

Use identities to find the values of the sine and cosine functions for the following angle measure.

Mathematics
1 answer:
puteri [66]1 year ago
6 0

Using the cosine double angle formula,

\cos 2\theta=2\cos^2 \theta-1=\frac{12}{13}\\\\2\cos^{2} \theta=\frac{25}{13}\\\\\cos^{2} \theta=\frac{25}{26}\\\\\boxed{\cos \theta=\frac{5}{\sqrt{26}}}

(Note I took the positive case since \theta terminates in the first quadrant)

Using the Pythagorean identity,

\sin^2 \theta+\cos^2 \theta=1\\\\\sin^2 \theta+\frac{25}{26}=1\\\\sin^2 \theta=\frac{1}{26}\\\\\boxed{\sin \theta=\frac{1}{\sqrt{26}}}

(Note I took the positive case since \theta terminates in the first quadrant)

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