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

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) $x = \frac { 7 \pi } { 4 }$

Quizplus · Accepted Answer

To solve for x in the equation $2\sin{x}-1=0,$ we first add 1 to both sides: $$2\sin{x}=1.$$Dividing by 2 gives $$\sin{x}=\frac{1}{2}.$$The solution for $x$ is any angle whose sine is $\frac{1}{2},$ which occurs at two angles in the interval $[0,2\pi),$ namely $\frac{\pi}{6}$ and $\frac{5\pi}{6}.$ Therefore, the correct answer is $\boxed{	extbf{(D) }\,x=\frac{5\pi}{6}}.$

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