Question

Solve Trig Equation


\( tan \theta = \frac{2\sqrt{3}}{3} sin \theta \)

Answer 1

I need to get the solution sets

Answer 2

hint u can write tan(theta) as sin(theta)/cos(theta)

Answer 3

Well, first off we should note that we cannot have solutions that would make cosine equal to 0, as then we would have something undefined. So let me change tangent into sin/cos and do this:
\[\frac{ \sin\theta }{ \cos\theta } = \frac{ 2\sqrt{3} }{ 3 }\sin\theta\]
\[\sin\theta = \frac{ 2\sqrt{3} }{ 3 }\sin\theta\cos\theta\]

\[\frac{ 2\sqrt{3} }{ 3 }\sin\theta\cos\theta - \sin\theta = 0\]

Now factor and see if you solve from there