Solve the equation in the interval [0°, 360°). Give solutions to the nearest tenth, if necessary.
-$2 \cos 2 \theta + 7 \sin \theta = 5$
A) $\left\{ 30 ^ { \circ } , 330 ^ { \circ } \right\}$
B) $\left\{ 90 ^ { \circ } , 48.6 ^ { \circ } , 131.4 ^ { \circ } \right\}$
C) $\left\{ 30 ^ { \circ } , 210 ^ { \circ } \right\}$
D) $\varnothing$

Question

Quizplus · Accepted Answer

This equation involves both $\cos 2\theta$ and $\sin \theta$, which suggests using trigonometric identities to simplify it. The identity $\cos 2\theta = 1 - 2\sin^2 \theta$ can be used to rewrite the equation in terms of $\sin \theta$ only. Substituting and solving the resulting quadratic equation in $\sin \theta$ yields solutions that correspond to the angles given in option B.

Solve the Equation in the Interval [0°, 360°) 2cos⁡2θ+7sin⁡θ=52 \cos 2 \theta + 7 \sin \theta = 52cos2θ+7sinθ=5

Solve the Equation in the Interval [0°, 360°) $2 \cos 2 \theta + 7 \sin \theta = 5$