Find the other 5 trig functions?

tan(θ) = −6,
sin(θ) > 0

1 Answer
Nghi N
Dec 15, 2017

tan t = - 6.
Find cos t by using the trig identity:
#cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 36) = 1/37#
#cos t = +- 1/sqrt37#.
Since tan t is negative and sin t > 0, therefor, cos t < 0.
#cos t = - 1/sqrt37 = - sqrt37/37#.
Find sin t.
#sin^2 t = 1 - cos^2 t = 1 - 1/37 = 36/37#
#sin t = 6/sqrt37 = 6sqrt37/37# (sin t > 0)
#cot t = 1/tan t = - 1/6 #
#sec t = 1/cos t = - sqrt37#
#csc t = 1/sin t = sqrt37/6#

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