The terminal side of #theta# in standard position contains (-8,-15), how do you find the exact values of the six trigonometric functions of #theta#?

1 Answer
Nghi N
May 23, 2018

Call t the arc (or angle). t lies in Quadrant 3
#tan t = y/x = -15/(-8) = 15/8#
#cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 225/64) = 64/289#
#cos t = +- 8/17#
Since t lies in Quadrant 3, cos t is negative
#cos t = - 8/17#
#sin^2 t = 1 - cos^2 t = 1 - 64/289 = 225/289#
#sin t = +- 15/17#
Since t is in Quadrant 3, sin t is negative
#sin t = - 15/17#
#tan t = sin t/(cos t) = (-15/17)(-17/8) = 15/8#
#cot = 1/(tan) = 8/15#
#sec = 1/(cos) = - 17/8#
#csc t = 1/(sin) = - 17/15#

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