Question

How do you find the solution to `9-2costheta=8-4costheta` if `0<=theta<2pi`?

Answer 1

`(2pi)/3 and (4pi)/3`

Explanation:

First solve the equation for `cos theta`, which would be

`2cos theta=-1`
`cos theta= -1/2`

In the given interval, `Cos theta` would be negative in IInd and IIIrd Quadrant. Therefore, as `cos (pi/3)=1/2`, cos (pi-pi/3) and cos (pi+pi/3) would be equal to `-1/2`. Thus the required answer is

`theta=(2pi)/3 and (4pi)/3`