Question #36b27

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Question #36b27

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Answer 1 · 2017-02-20T22:40:51

#120/169#

Explanation:

#tan t = 5/12# --> #cot t = 12/5#
Use trig identity:
#sin^2 t = 1/(1 + cot^2 t)\sin^2 t = 1/(1 + 144/25) = 25/169#
#sin t = +- 5/13#
Since t is in Quadrant 3, there for, sin t is negative
#sin t = - 5/13#.
Find cos t.
#co^2 t = 1 - sin^2 t = 1 - 25/169 = 122/169#
#cos t = - 12/13# (t in Quadrant III)
#sin 2t = 2sin t.cos t = 2(-5/13)(-12/13) = 120/169#

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Question #36b27

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