Answer
Refer to the graph below.
Work Step by Step
RECALL:
The functions $y=a \cdot \sin{bx}$ and $y=a \cdot \cos{bx}$ have:
period = $\dfrac{2\pi}{b}$
amplitude = $|a|$
The given function has $a=-2$ and $b=3$ thus
period = $\dfrac{2\pi}{3}=\dfrac{2}{3}\pi$
amplitude = $|-2| = 2$
To graph the function, perform the following steps:
(1) With a period of $\frac{2}{3}\pi$, one period of the function is over the interval $[0, \frac{2}{3}\pi]$.
(2) Divide this interval into four parts to obtain the x-values $0, \frac{1}{6}\pi, \frac{1}{3}\pi, \frac{1}{2}\pi, \text{ and } \frac{2}{3}\pi$.
(3) Make a table of values using the x-values above. (Refer to the table below.)
(4) Plot the five points of the table of values then connect them using a sinusoidal curve whose amplitude is $2$.
(5) Repeat the cycle of the graph form one more period, which is $[\frac{2}{3}\pi, \frac{4}{3}\pi]$.
(Refer to the graph in the answer part above.)
