Question

How do you use the point (-12,3) on the terminal side of the angle to evaluate the six trigonometric functions?

Answer 1

`tan t = y/x = 3/-12 = - 1/4`
The terminal side of t is in Quadrant 3.
`cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 1/16) = 16/17`
`cos t = - 4/sqrt17`
`sin t = tan t.cos t = (-1/4)(-4/sqrt17) = 1/sqrt17`
`cot t = 1/(tan t) = - 4`
`sec t = 1/(cos t) = - sqrt17/4`
`csc t = 1/(sin t) = sqrt 17`