Use Identities to Solve Trigonometric Equations
Solve the equation on the interval [0, 2π).
-$\sin \left( x + \frac { 7 \pi } { 6 } \right) - \sin \left( x - \frac { 7 \pi } { 6 } \right) = 1$
A) $\pi$
B) $\frac { \pi } { 2 } , \frac { \pi } { 4 }$
C) $\frac { \pi } { 4 } , \frac { \pi } { 3 }$
D) $\frac { \pi } { 2 } , \frac { \pi } { 3 }$

Question

Quizplus · Accepted Answer

Using the sine addition and subtraction identities, the equation simplifies to $2 \cos(x) \sin(\frac{7\pi}{6}) = 1$. Since $\sin(\frac{7\pi}{6}) = -\frac{1}{2}$, the equation becomes $-\cos(x) = \frac{1}{2}$, which has a solution at $x = \pi$.

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

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