How do you find all six trigonometric function of #theta# if the point (3,4) is on the terminal side of #theta#?

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How do you find all six trigonometric function of #theta# if the point (3,4) is on the terminal side of #theta#?

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Answer 1 · 2017-03-20T15:19:47

The terminal side, containing point (3, 4) is located in Quadrant 1.
Call t the angle:
#tan t = y/x = 4/3#
#cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 16/9) = 9/25#
#cos t = 3/5# (t in Quadrant 1 --> cos t is positive)
#sin^2 t = 1 - cos^2 t = 1 - 9/25 = 16/25#
#sin t = 4/5# (t in Quadrant 1 --> sin t is positive)
#tan t = 4/3#
#cot t = 1/(tan t) = 3/4#
#sec t = 1/(cos t) = 5/3#
#csc t = 1/(sin t) = 5/4#

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How do you find all six trigonometric function of #theta# if the point (3,4) is on the terminal side of #theta#?

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