How do you find all six trigonometric function of #theta# if the point #(-9a, -12a)# is on the terminal side of #theta#?

1 Answer
Nov 23, 2017

Answer:

cos t = - 3/5
sin t = - 4/5
cot t = 3/4
sec t = - 5/3
csct = - 5/4

Explanation:

t is in Quadrant 3.
#tan t = y/x = -12a/-9a = 4/3#
#cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 16/9) = 9/25#
#cos t = +- 3/5#
Since t is in Quadrant 3, take the negative answer.
#sin^2 t = 1 - cos^2 t = 1 - 9/25 = 16/25#.
#sin t = +- 4/5#
Take the negative answer, because t is in Q. 3.
#cot t = 3/4#
#sec t = 1/(cos t) = - 5/3#
#csc t = 1/(sin t) = - 5/4#