Question

How do you find the solution to `3tantheta-1=tantheta+9` if `0<=theta<2pi`?

Answer 1

Rearrange.

`θ approx 1.37340077 rad`

Explanation:

`3tantheta-1=tantheta+9`
`0 leq θ < 2pi`

Start by rearranging.

`3tantheta-1=tantheta+9`
`3tantheta=tantheta+10` //add 1 to both sides
`2tantheta=10` // subtract `tantheta` from both sides
`tantheta=5` // divide both sides by 2
`theta=arctan5` // arctan on both sides, (`arctan(tan(theta))= theta`)

`θ approx 1.37340077 rad`