Question

3sin x=2/sinx

Answer 1

Have you considered factoring?

1) \(\sin(x) \ne 0\)

\(3\sin^{2}(x) - 2 = 0\)

\((\sqrt{3}\sin(x) - \sqrt{2})(\sqrt{3}\sin(x) + \sqrt{2}) = 0\)

You're almost done!

Answer 2

Factoring is not necessary

Answer 3

\[\Large\begin{array}{rcl}
3\sin x&=&\frac2{\sin x}\\
\sin^2x&=&\frac23\\
\sin x&=&\sqrt{\frac23}
\end{array}\]

Answer 4

No good. You missed the negative solution. I guess factoring was necessary.

Answer 5

\[\large\begin{array}{rcl}
3\sin x&=&\frac2{\sin x}\\
\sin^2 x&=&\frac23\\
\sin x=\frac23&or&\sin x=-\frac23
\end{array}\]

Answer 6

Never much liked the "remember to include the negative" idea. Factoring just hands it to you. No forgetting allowed.