Question

Question #06337

Answer 1

`theta=60^circ=pi/3`

Explanation:

We can rearrange this equation to get: `2cos^2theta=costheta`

We have like terms on each side that we can divide by.

`(2cos^2theta)/costheta=costheta/costheta`

`(2cos^cancel(2)theta)/cancel(costheta)=cancel(costheta)/cancel(costheta)`

`2costheta=1`

`costheta=1/2`

`theta=cos^(-1)(1/2)=60^circ=pi/3`

Answer 2

`theta=pi/3`

Explanation:

`"take out a common factor of "costheta`

`rArrcostheta(2costheta-1)=0`

`rArrcostheta=0rArrtheta=pi/2+2kpi;k inZZ`

`"or "costheta=1/2rArrtheta=pi/3+2kpi;k inZZ`

`"smallest positive value is "theta=pi/3`