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k8lyn911
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?
\[ 6 \sin (\theta )-3 \csc (\theta )=6 \sin (\theta )-\frac{3}{\sin (\theta )}=\frac{6 \sin ^2(\theta )-3}{\sin (\theta )}=0 \]
\[ \left\{\sin (\theta )= -\frac{1}{\sqrt{2}}\right\},\left\{\sin (\theta )= \frac{1}{\sqrt{2}}\right\} \]
\[ \theta=\frac \pi 4\\ \theta =\pi -\frac \pi 4=\frac { 3 \pi}4\\ \theta =\frac{5 \pi}4\\ \theta =\frac{7 \pi}4\\ \]