Solve the equation in the interval [0°, 360°). Give solutions to the nearest tenth, if necessary.
-$\sin 2 \theta = - \sin \theta$
A) $\left\{ 0 ^ { \circ } , 120 ^ { \circ } , 180 ^ { \circ } , 240 ^ { \circ } \right\}$
B) $\left\{ 0 ^ { \circ } , 180 ^ { \circ } \right\}$
C) $\left\{ 0 ^ { \circ } , 60 ^ { \circ } , 120 ^ { \circ } , 180 ^ { \circ } , 240 ^ { \circ } , 300 ^ { \circ } \right\}$
D) $\left\{ 60 ^ { \circ } , 120 ^ { \circ } , 240 ^ { \circ } , 300 ^ { \circ } \right\}$

Question

Quizplus · Accepted Answer

Using the identity $\sin 2\theta = 2\sin \theta \cos \theta$, the equation becomes $2\sin \theta \cos \theta = -\sin \theta$. Solving this equation for $\theta$ in the interval [0°, 360°) gives the solutions $0^\circ, 120^\circ, 180^\circ,$ and $240^\circ$.

Solve the Equation in the Interval [0°, 360°) sin⁡2θ=−sin⁡θ\sin 2 \theta = - \sin \thetasin2θ=−sinθ

Solve the Equation in the Interval [0°, 360°) $\sin 2 \theta = - \sin \theta$