Question

solve the given equation. (enter your answers as a comma-separated list. let k be any inte
\\( \sin \theta = \frac{\sqrt{3}}{2} \\)
\\( \theta = \\) \\( \times \\) rad

Explanation:

Step1: Recall sine values

We know that $\sin\frac{\pi}{3}=\frac{\sqrt{3}}{2}$ and $\sin(\pi - \frac{\pi}{3})=\sin\frac{2\pi}{3}=\frac{\sqrt{3}}{2}$.

Step2: General solution for sine

The general solution for $\sin\theta = \sin\alpha$ is $\theta=\alpha + 2k\pi$ or $\theta=\pi-\alpha + 2k\pi$, where $k\in\mathbb{Z}$. Here $\alpha=\frac{\pi}{3}$, so the solutions are $\theta=\frac{\pi}{3}+2k\pi,\frac{2\pi}{3}+2k\pi$.

Answer:

$\frac{\pi}{3}+2k\pi,\frac{2\pi}{3}+2k\pi$