## Algebra and Trigonometry 10th Edition

The graph of $sin~6x$ with two periods is shown below.
The period of $sin~x$ is $2\pi$. We want two periods ($4\pi$). Then, $0\lt6x\lt4\pi$ $0\lt x\lt\frac{2\pi}{3}$ Maximum: $sin~6x=1$ $6x=\frac{\pi}{2}$ and $6x=\frac{5\pi}{2}$ $x=\frac{\pi}{12}$ and $x=\frac{5\pi}{12}$ Minimum: $sin~6x=-1$ $6x=\frac{3\pi}{2}$ and $6x=\frac{7\pi}{2}$ $x=\frac{3\pi}{12}$ and $x=\frac{7\pi}{12}$