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 $b=2\pi$ thus
period = $\dfrac{2\pi}{2\pi}=1$
amplitude = $|-2| = 2$
To graph the function, perform the following steps:
(1) With a period of $1$, one period of the function is over the interval $[0, 1]$.
(2) Divide this interval into four parts to obtain the x-values $0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, \text{ and } 1$.
(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 $[1, 2]$.
(Refer to the graph in the answer part above.)
