How do you find the exact values of the six trigonometric function of #theta# if the terminal side of #theta# in the standard position contains the point (4,-3)?

1 Answer
Jun 10, 2018

Coordinates of the point on the terminal side:
x = 4 and y = -3. The point lies in Quadrant 4.
Call t the angle (arc):
#tan t = y/x = - 3/4#
#cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 9/16) = 16/25#
#cos t = 4/5# (because t lies in Quadrant 4)
#sin t = tan t.cos t = (-3/4)(4/5) = - 12/20 = - 3/5#
#cot = 1/tan = - 4/3#
#sec t = 1/cos = 5/4#
#csc t = 1/sin = -5/3#