Find two values of q that satisfy the equation below. Give values of q in radians $( 0 \leq \theta \leq 2 \pi )$ . Do not use a calculator. sin q = $- \frac { \sqrt { 3 } } { 2 }$
A) $\theta = \frac { \pi } { 3 },$ $\theta = \frac { 5 \pi } { 3 }$
B) $\theta = \frac { \pi } { 3 },$ $\theta = \pi$
C) $\theta = \frac { 4 \pi } { 3 }$ , $\theta = \frac { 5 \pi } { 3 }$
D) $\theta = \frac { \pi } { 6 },$ $\theta = \frac { 7 \pi } { 6 }$
E) $\theta = \frac { \pi } { 3 }$, $\theta = \frac { 5 \pi } { 3 }$

Question

Quizplus · Accepted Answer

The sine function equals $-\frac{\sqrt{3}}{2}$ at angles where the sine is negative, which occurs in the third and fourth quadrants. The reference angle for $\sin(\theta) = -\frac{\sqrt{3}}{2}$ is $\frac{\pi}{3}$, so the angles in the specified range are $\frac{4\pi}{3}$ and $\frac{5\pi}{3}$.

Find Two Values of Q That Satisfy the Equation Below (0≤θ≤2π)( 0 \leq \theta \leq 2 \pi )(0≤θ≤2π)

Find Two Values of Q That Satisfy the Equation Below $( 0 \leq \theta \leq 2 \pi )$