Question #49b70

1 Answer
Nghi N.
Mar 20, 2017

#cos 2t = -119/169#
#tan 2t = 120/119#

Explanation:

#tan t = - 12/5#, t is in Quadrant 2.
#cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 144/25) = 25/169#
#cos t = - 5/13# (cos t is negative, t in Quadrant 2)
#sin^2 t = 1 - cos^2 t = 1 - 25/169 = 144/169#
#sin t = 12/13# (sin t is positive)
#sin 2t = 2sin t.cos t = 2(12/13)(-5/13) = -120/169 #
#cos 2t = 2cos^2 t - 1 = 50/169 - 1 = - 119/169#
#tan 2t = (sin 2t)/(cos 2t) = (- 120/169)(- 169/119)#
#tan 2t = 120/119#

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