Question

How do you use the point `(1,-sqrt3)` on the terminal side of the angle to evaluate the six trigonometric functions?

Answer 1

Call t the angle (arc)
`tan t = y/x = - sqrt3/1 = - sqrt3`.
t is in Quadrant 4.
Trig table and unit circle give -->
`t = (2pi)/3 + pi = (5pi)/3`
#sin t = sin (5pi)/3 = sin (2pi - pi/3) = sin (-pi/3) = = - sin (pi/3) = - sqrt3/2#
`cos t = cos (- pi/3) = cos pi/3 = 1/2`
`cot t = 1/(tan) = - 1/sart3 = - sqrt3/3`
`sec t = 1/(cos) = 2`
`csc t = 1/(sin) = - 2/sqrt3 = - (2sqrt3)/3`