Question

If `costheta=5/13` and `theta` is in the fourth quadrant, what is `sin` and `tan theta`?

`costheta=5/13`

Answer 1

`sin t = - 12/13`
`tan t = -12/5`

Explanation:

`cos t = 5/13`
`sin^2 t = 1 - cos^2 t = 1 - 25/169 = 144/169`
`sin t = +- 12/13`
Since t is in Quadrant 4, therefor, sin t is negative
`sin t = -12/13`
`tan t = sin t/(cos t) = (-12/13)(13/5) = - 12/5`