How do you find the values of the six trigonometric functions of an angle in standard position if a point with #(5, -3)# has on its terminal side?

1 Answer
Nghi N
Mar 7, 2018

Call t the angle. The terminal side of t is in Quadrant 4.
#tan t = y/x = -3/5#
#cos^2 t = 1/(1 + tan^2 t = 1/(1 + 9/25) = 25/34#
#cos t = +- 5/sqrt34#
Since t is in Quadrant 4, then, cos t is positive
#cos t = 5/sqrt34#
#sin t = tan t.cos t = (-3/5)(5/sqrt34) = -3/sqrt34#
#cot t = - 5/3#
#sec t = sqrt34/5#
#csc t = - sqrt34/3#

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