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
Nghi N.
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

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