Question

Two solutions of the equation $\sin \theta =\frac{1}{2}$are ____ and ____.

Short answer

Two solutions of the equation $\sin \theta =\frac{1}{2}$are $\frac{\mathrm{\pi }}{6}\mathrm{and}\frac{5\mathrm{\pi }}{6}$.

Step-by-step solution

Step 1. Given Information

Two solutions of the equation$\sin \theta =\frac{1}{2}$ are ____ and ____.

Step 2. The period of the sine function is 2π.

In the interval $[0,2\mathrm{\pi })$, there are two angles $\theta$ for which

$\sin \theta =\frac{1}{2}:\theta =\frac{\pi }{6},\theta =\frac{5\pi }{6}$

Two solution of$\sin \theta =\frac{1}{2}$are$\frac{\mathrm{\pi }}{6}\mathrm{and}\frac{5\mathrm{\pi }}{6}$