If #sin theta = - 3/5# and #180° < theta < 270°#, what is #tan 2theta#?

1 Answer
Nghi N.
Nov 6, 2015

Find tan 2x knowing #sin x = -3/5# and 180 < x < 270.

Ans: #24/7#

Explanation:

#sin x = - 3/5#. First, find cos x.
#cos^2 x = 1 - sin^2 x = 1 - 9/25 = 16/25# --> #cos x = +- 4/5#.
Since arc x is located in Quadrant III, then both sin x and cos x are negative --> #cos x = -4/5#.
#sin 2x = 2sin x.cos x = 2(-3/5)(-4/5)= 24/25#
#cos 2x = 1 - 2sin^2 x = 1 - 18/25 = 7/25#
#tan 2x = (sin 2x)/(cos 2x) = (24/25)(25/7) = 24/7#

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