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

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

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Answer 1 · 2015-11-18T16:09:16

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#

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

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