Use Identities to Solve Trigonometric Equations
Solve the equation on the interval [0, 2π).
-$\sin 2 x + \sin x = 0$
A) $0 , \frac { 2 \pi } { 3 } , \pi , \frac { 4 \pi } { 3 }$
B) $\frac { \pi } { 8 } , \frac { 9 \pi } { 8 }$
C) $\frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }$
D) no solution

Question

Quizplus · Accepted Answer

Using the double angle identity, $\sin 2x = 2\sin x \cos x$, the equation becomes $2\sin x \cos x + \sin x = 0$. Factoring out $\sin x$, we get $\sin x(2\cos x + 1) = 0$. Setting each factor to zero gives the solutions $x = 0, \frac{2\pi}{3}, \pi, \frac{4\pi}{3}$ within the interval [0, 2π).

Use Identities to Solve Trigonometric Equations Solve the Equation on the Interval

Use Identities to Solve Trigonometric Equations
Solve the Equation on the Interval