Find all solutions of the following equation in the interval [0,2π). $\sin ^ { 3 } x = \sin x$
A) $x = 0 , \frac { \pi } { 6 } , \frac { 7 \pi } { 6 }$
B) $x = 0 , \frac { \pi } { 4 } , \frac { 7 \pi } { 4 }$
C) $x = 0 , \frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$
D) $x = 0 , \pi$
E) $x = 0 , \frac { \pi } { 2 } , \pi , \frac { 3 \pi } { 2 }$

Question

Find all solutions of the following equation in the interval [0,2π).​ $\sin ^ { 3 } x = \sin x$ ​
A) $x = 0 , \frac { \pi } { 6 } , \frac { 7 \pi } { 6 }$
B) $x = 0 , \frac { \pi } { 4 } , \frac { 7 \pi } { 4 }$
C) $x = 0 , \frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$
D) $x = 0 , \pi$
E) $x = 0 , \frac { \pi } { 2 } , \pi , \frac { 3 \pi } { 2 }$

Quizplus · Accepted Answer

The equation $\sin^3 x = \sin x$ can be simplified to $\sin x(\sin^2 x - 1) = 0$, which further simplifies to $\sin x(\cos^2 x) = 0$. This equation is satisfied when $\sin x = 0$ or $\cos x = 0$, which corresponds to $x = 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}$ within the interval $[0, 2\pi)$.

Find All Solutions of the Following Equation in the Interval sin⁡3x=sin⁡x\sin ^ { 3 } x = \sin xsin3x=sinx

Find All Solutions of the Following Equation in the Interval $\sin ^ { 3 } x = \sin x$