Question

How do you determine `costheta` given `sintheta=-1/5,pi<theta<(3pi)/2`?

Answer 1

`cos theta= -(2sqrt6)/5`

Explanation:

`theta` is in 3rd quadrant where both `sin theta and cos theta`

is negative. `sin theta = 1/-5 :. sin^2 theta = 1/25`

`cos theta = +-sqrt(1-sin^2 theta) = +-sqrt (1-1/25) =+-sqrt 24/5`

Since `cos theta` is negative in 3rd quadrant ,

`cos theta= -sqrt 24/5 or cos theta= -(2sqrt6)/5` [Ans]