# Chapter 4 - Graphs of the Circular Functions - Section 4.1 Graphs of the Sine and Cosine Functions - 4.1 Exercises - Page 149: 27 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 $b=3$ thus period = $\dfrac{2\pi}{3}=\dfrac{2}{3}\pi$ amplitude = $|1| = 1$ 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 ampliude is $1$. (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.) 