Question

How do you find the five remaining trigonometric function satisfying `tantheta=-12/5`, `sintheta>0`?

Answer 1

cos^2 t = 1/(1 + tan^2 t) = 1/(1 + 144/25) = 25/169
`cos t = +- 5/13`
`sin t = (tan t)(cos t) = (-12/5)(- 5/13) = 12/13`
Note. tan t < 0 and sin t > 0, then, cos t < 0)
`cot t = 1/(tan) = - 5/12`
`sec t = 1/(cos) = - 13/5`
`csc t = 1/(sin) = 13/12`