Question

Given `csctheta=-5, costheta<0` to find the remaining trigonometric function?

Answer 1

`csc t = 1/(sin t) = - 5` --> `sin t = - 1/5`
`cos^2 t = 1 - sin^2 t = 1 - 1/25 = 24/25`
`cos t = - 2sqrt6/5` --> (cos t < 0)
`tan t = sin/(cos) = (-1/5)(5/(-2sqrt6)) = 1/(2sqrt6) = sqrt6/12`
`cot t = 1/(tan) = 12/sqrt6 = 12sqrt6/6 = 2sqrt6`
`sec t = 1/(cos) = - 5/(2sqrt6) = - (5sqrt6)/12)`