Question

What is the value of `costheta` if `sintheta=1/2` and `theta` is in `Q2`?

Answer 1

`costheta=-sqrt3/2`

Explanation:

As domain of `theta` is `90^o< theta<180^o`,

while `sintheta` is positive, `costheta` is negative.

As `sintheta=1/2`, and `sin^2theta+cos^2theta=1`

we have `cos^2theta=1-sin^2theta` and as `costheta` is negative

`costheta=-sqrt(1-sin^2theta)=-sqrt(1-(1/2)^2)`

= `-sqrt(1-1/4)=-sqrt(3/4)=-sqrt3/2`