Question

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

θ, given that cos 20 =12/13 and θ terminates in quadrant I. Find sin θ and cos θ. Can you explain how do it and what is the answer?

Answer 1

Using the cosine double angle formula,

`\cos 2\theta=2\cos^2 \theta-1=(12)/(13)\\\\2\cos^(2) \theta=(25)/(13)\\\\\cos^(2) \theta=(25)/(26)\\\\\boxed{\cos \theta=(5)/(√(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+(25)/(26)=1\\\\sin^2 \theta=(1)/(26)\\\\\boxed{\sin \theta=(1)/(√(26))}`

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