Use inverse functions where needed to find all solutions of the equation in the interval [0, 2π).
B)
C)
D)

Question

Use inverse functions where needed to find all solutions of the equation in the interval [0, 2π). ​  ​
B)​ 
C)​ 
D)​

Quizplus · Accepted Answer

First, we can rewrite the equation as $\sin(x) = \frac{\sqrt{3}}{2}$. Taking the inverse sine of both sides, we have $x = \frac{\pi}{3} + 2\pi n$ or $x = \frac{2\pi}{3} + 2\pi n$ for some integer $n$. However, we need to restrict the solutions to the interval $[0, 2\pi)$. The solutions in this interval are $\frac{\pi}{3}$ and $\frac{5\pi}{3}$. It is important to note that the solution $x = \frac{2\pi}{3}$ lies outside of the specified interval. Therefore, the only solution in the interval is $\frac{\pi}{3}$, so the answer is choice C.

Use Inverse Functions Where Needed to Find All Solutions of the Equation