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 $a=1$ and $b=\frac{2}{3}$ thus
period = $\dfrac{2\pi}{\frac{2}{3}}=3\pi$
amplitude = $|1| = 1$
To graph the function, perform the following steps:
(1) With a period of $3\pi$, one period of the function is over the interval $[0, 3\pi]$.
(2) Divide this interval into four parts to obtain the x-values $0, \frac{3}{4}\pi, \frac{3}{2}\pi, \frac{9}{4}\pi, \text{ and } 3\pi$.
(3) Make a table of values using the x-values above. (Refer to the table below.)
(4) Plot the five points of the tanle of values then connect them using a sinusoidal curve whose ampliude is $1$.
(5) Repeat the cycle of the graph form one more period, which is $[3\pi, 6\pi]$.
(Refer to the graph in the answer part above.)
