Solve the equation in the interval [0°, 360°). Give solutions to the nearest tenth, if necessary.
-$3 \sin ^ { 2 } \theta - \sin \theta - 4 = 0$
A) $\left\{ 0 ^ { \circ } \right\}$
B) $\left\{ 270 ^ { \circ } \right\}$
C) $\left\{ 180 ^ { \circ } \right\}$
D) $\left\{ 90 ^ { \circ } \right\}$

Question

Quizplus · Accepted Answer

The equation can be rewritten as a quadratic in terms of $\sin \theta$: $3x^2 - x - 4 = 0$, where $x = \sin \theta$. Solving this quadratic gives no real solutions for $\sin \theta$ in the interval $[-1, 1]$, except at $\theta = 270^\circ$ where $\sin \theta = -1$.

Solve the Equation in the Interval [0°, 360°) 3sin⁡2θ−sin⁡θ−4=03 \sin ^ { 2 } \theta - \sin \theta - 4 = 03sin2θ−sinθ−4=0

Solve the Equation in the Interval [0°, 360°) $3 \sin ^ { 2 } \theta - \sin \theta - 4 = 0$