Question

How do you find the 6 trigonometric functions at the angle `Θ = tan^(-1) (-5/12)`?

Answer 1

Consider the right triangle OmM, with
horizontal side Om = 12
vertical side mM = -5
Hypotenuse `OM = sqrt(144 + 25) = sqrt169 = 13`
Call t --> the angle < mOM:
`sin t = - 5/13`
`cos t = 12/13`
`tan t = - 5/12`
`cot = - 12/5`
`sec t = 13/12`
`csc t = - 13/5`