Question

How do you find the exact values of `costheta` and `tantheta` when `sintheta=-2/3`?

Answer 1

`costheta= +- sqrt5/3` and `tantheta=+- (2sqrt5)/5`

Explanation:

Use trig identity:
`cos^2 theta = 1 - sin^2 theta`
`cos ^2theta = 1 - 4/9 = 5/9`
`cos theta = +- sqrt5/3`
`tan theta = sintheta/(cos theta) = +- (2/3)(3/sqrt5) = +- 2/sqrt5 = +- (2sqrt5)/5`