Find the exact value of sin2(θ) and quadrant where it is if cosθ=-(4/5) with θ in quadrant II?

Any help is much appreciated.

1 Answer
Nghi N
Apr 2, 2018

#sin 2t = - 24/25#
2t is in Quadrant 3.

Explanation:

#cos t = - 4/5#
#sin^2 t = 1 - cos^2 t = 1 - 16/25 = 9/25#
#sin t = +- 3/5#
Since t is in Quadrant 2, then sin t is positive.
#sin 2t = 2sin t.cos t = 2(3/5)(- 4/5) = -24/25#.
2t is in Quadrant 3.

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