Answer: Key points include \(\left(-\frac{\pi}{3},-2\right)\), \(\left(-\frac{\pi}{6},-6\right)\), \((0,-2)\), \(\left(\frac{\pi}{6},2\right)\), and \(\left(\frac{\pi}{3},-2\right)\).
Answer: Key points include \(\left(-\frac{\pi}{3},-2\right)\), \(\left(-\frac{\pi}{6},-6\right)\), \((0,-2)\), \(\left(\frac{\pi}{6},2\right)\), and \(\left(\frac{\pi}{3},-2\right)\).
The graph is
\(y=4\sin3x-2.\)
The midline is
\(y=-2,\)
and the amplitude is \(4\). Therefore the maximum value is \(2\) and the minimum value is \(-6\).
The period is
\(\frac{2\pi}{3}.\)
On the interval \(-\frac{\pi}{3}\leq x\leq\frac{\pi}{3}\), one complete cycle is shown. Useful key points are
\(\left(-\frac{\pi}{3},-2\right),\quad \left(-\frac{\pi}{6},-6\right),\quad (0,-2),\quad \left(\frac{\pi}{6},2\right),\quad \left(\frac{\pi}{3},-2\right).\)
