Question

How do you find sin 2θ, given cos θ = 5/13 and θ lies in Quadrant IV?

Answer 1

Find sin 2x, knowing `cos x = 5/13`

Ans: `-120/169`

Explanation:

`cos x = 5/13.` Find sin x.
`sin^2 x = 1 - cos^2 x = 1 - 25/169 = 144/169` --> `sin x = +- 12/13`.
Since x is in Quadrant IV, then sin x is negative.
`sin x = - 12/13`.
`sin 2x = 2sin x.cos x = 2(-12/13)(5/13) = -120/169`