How does one find sin2x, cos2x, and tan2x if x is in quadrant IV and equals -2/#sqrt13#?

1 Answer
Nghi N
May 17, 2018

#sin 2x = - 12/13#
#cos 2x = 5/13#
#tan 2x = - 12/5#

Explanation:

#sin x = - 2/sqrt13# (x is in Quadrant 4). Find cos x
#cos ^2 x = 1 - sin^2 x = 1 - 4/13 = 9/13#
#cos x = 3/(sqrt13)# (because x is in Q. 4)
#sin 2x = 2sin x.cos x = 2(-2/sqrt13)(3/sqrt13) = -12/13#
#cos^2 2x = 1 - sin^2 2x = 1 - 144/169 = 25/169#
#cos 2x = 5/13#
#tan 2x = (sin 2x)/(cos 2x) = (-12/13)(13/5) = - 12/5#

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