Question

How do you find the five remaining trigonometric function satisfying `csctheta=-3/2`, `costheta<0`?

Answer 1

`csc t = 1/(sin t) = - 3/2` --> `sin t = - 2/3`
`sin t = - 2/3`
`cos^2 t = 1 - sin^2 t = 1 - 4/9 = 5/9` --> `cos t = +- sqrt5/3`
`cos t = - sqrt5/3` (cos t < 0)
`tan t = sin/(cos) = (- 2/3)(- 3/sqrt5) = 2/sqrt5 = (2sqrt5)/5`
`cot t = 1/(tan t) = 5/(2sqrt5)`.
`sec t = 1/(cos) = - 3/sqrt5 = - (3sqrt5)/5`.
`csc t = -3/2`