How do you use the point (-9,14) on the terminal side of the angle to evaluate the six trigonometric functions?

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Nghi N. Share
Mar 19, 2017

The terminal side, containing point (-9, 14), is in Quadrant 3.
Call t the angle.
#tan t = -14/9#
#cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 196/81) = 81/277#
#cos t = +- 9/sqrt277#
Because t is in Quadrant 3, cos t is negative -->
#cos t = - 9/(sqrt277)#
#sin t = tan t.cos t = (-14/9)(-9/sqrt277) = 14/sqrt277#
#tan t = -14/9#
#cot t = - 9/14#
#sec t = 1/(cos) = - sqrt277/9#
#csc t = 1/(sin) = sqrt277/14#

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