Solve the equation for solutions in the interval [0, 2 $$[ 0,2 \pi ) \text {. }$$
-$$\sin 4 x = \frac { \sqrt { 3 } } { 2 }$$
A) $\left\{ \frac { \pi } { 4 } , \frac { 5 \pi } { 4 } \right\}$
B) $\left\{ \frac { \pi } { 12 } , \frac { \pi } { 6 } , \frac { 2 \pi } { 3 } , \frac { 7 \pi } { 12 } , \frac { 7 \pi } { 6 } , \frac { 13 \pi } { 12 } , \frac { 5 \pi } { 3 } , \frac { 19 \pi } { 12 } \right\}$
C) $\left\{ 0 , \frac { \pi } { 4 } , \pi \right\}$
D) $\{ 0 \}$

Question

Quizplus · Accepted Answer

The equation $\sin 4x = \frac{\sqrt{3}}{2}$ has solutions where the sine function equals $\frac{\sqrt{3}}{2}$, which occurs at angles of $\frac{\pi}{3}$ and $\frac{2\pi}{3}$ in the first revolution. Since the argument of the sine function is $4x$, we divide these angles by 4 to find the solutions in one revolution, and then find all solutions in the interval $[0, 2\pi)$ by considering the periodicity and symmetry of the sine function. This results in eight solutions, as listed in option B.

Solve the Equation for Solutions in the Interval [0, 2 [0,2π). [ 0,2 \pi ) \text {. }[0,2π).

Solve the Equation for Solutions in the Interval [0, 2 $[ 0,2 \pi ) \text {. }$