Which of the following is a solution to the given equation?
$2 \sin x - 1 = 0$
A) $x = \frac { 7 \pi } { 6 }$
B) $x = \frac { 2 \pi } { 3 }$
C) $x = \frac { 3 \pi } { 4 }$
D) $x = \frac { 5 \pi } { 6 }$
E) $x = \frac { 7 \pi } { 4 }$

Question

Quizplus · Accepted Answer

We must isolate sin x to solve for x. Adding 1 to both sides, we get $2\sin x = 1$. Dividing by 2 gives $\sin x = \frac{1}{2}$. The only angle in the interval $[0,2\pi)$ that has a sine of $\frac{1}{2}$ is $\frac{\pi}{6}$ or $ \frac{5\pi}{6}$. Since $2\pi$ added to either of these angles will give us another solution, we can also add $2\pi$ to obtain $\frac{7\pi}{6}$ and $ \frac{11\pi}{6}$ as solutions. The only one of these solutions in the answer choices is $\frac{5\pi}{6}$.

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Which of the Following Is a Solution to the Given $2 \sin x - 1 = 0$