Question

How do you use the point (15,-8) on the terminal side of the angle to evaluate the six trigonometric functions?

Answer 1

Find trig functions by using trig identities.
Point (15, -8) is in Quadrant 4.
`tan t = y/x = - 8/15`
`cot t = - 15/8`
Find cos t by the identity:
`cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 64/225) = 225/289`
`cos t = 15/17` (because t is in quadrant 4)
Find sin t by the identity:
`sin^2 t = 1/(1 + cot^2 t) = 1/(1 + 225/64) = 64/289`
`sin t = - 8/17` (because t is in Quadrant 4)
`sec t = 1/cos t = 17/15`
`csc t = 1/sin t = 17/8`