Question

How do you use the point (6,-9) on the terminal side of the angle to evaluate the six trigonometric functions?

Answer 1

Find values of trig functions

Explanation:

Consider the right triangle OmM.
Om = x = 6, and mM = y = - 9
Hypotenuse `OM = sqrt(36 + 81) = sqrt117`
Call t the angle <mOM
`sin t = -9/(sqrt117)`
`cos t = 6/(sqrt117)`
`tan t = -9/6 = -3/2`
`cot t = 1/(tan) - 2/3`
`sec t = 1/(cos) = sqrt117/6`
`csc t = 1/(sin) = - sqrt117/9`