Question

6 sin θ − 3 csc θ = 0

Solve the equation for θ if 0° ≤ θ < 360°.
(Enter your answers as a comma-separated list.)

*Okay, so I know csc θ = 1/sin θ

6 sin θ - 3 csc θ = 0
6 sin θ - (3/sin θ) = 0
3 sin θ (2 - ? ) = 0

That's where I got stuck.
How do I simplify it further to find the answer?

Answer 1

\[
6 \sin (\theta )-3 \csc (\theta )=6 \sin
(\theta )-\frac{3}{\sin (\theta )}=\frac{6
\sin ^2(\theta )-3}{\sin (\theta )}=0

\]

Answer 2

\[
\left\{\sin (\theta )=
-\frac{1}{\sqrt{2}}\right\},\left\{\sin
(\theta )=
\frac{1}{\sqrt{2}}\right\}
\]

Answer 3

\[
\theta=\frac \pi 4\\
\theta =\pi -\frac \pi 4=\frac { 3 \pi}4\\
\theta =\frac{5 \pi}4\\
\theta =\frac{7 \pi}4\\

\]

Answer 4

Thank you! :)

Answer 5

YW