Question

Given that sin t=(-2/3) and that P(t) is a point in the third quadrant, what is cos (t)?

Answer 1

`cos t = sqrt5/3`

Explanation:

`sin^2 t + cos^2 t = 1`

Given that `sin t = -2/3`
`sin^2t = (-2/3)^2=4/9`

Therefore `cos^2t = 1-4/9 = 5/9`

`cos t = ± {sqrt5}/3`

Since cos is negative in the third quadrant we can rule out the positive solution.

Therefore `cos t = sqrt5/3`