Question

How do you find the solution to `3tan^2theta=1` if `0<=theta<360`?

Answer 1

`\theta=30,210,150,330`

Explanation:

`tan^{2}\theta = \frac{1}{3}`

Therefore:

`tan\theta=+-\frac{1}{\sqrt{3}}`

Solutions cna be found such that:

`\theta=tan^{-1}(\frac{1}{\sqrt{3}})=30, 210` Using the 180 cycle in a tan graph.

doing the same for the negation version gives us:
`\theta=tan^{-1}(-\frac{1}{\sqrt{3}})=cancel(-30),150,330`

therefore all the solutions are:
`\theta=30,210,150,330`