# Chapter 4 - Graphs of the Circular Functions - Section 4.1 Graphs of the Sine and Cosine Functions - 4.1 Exercises - Page 149: 26

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 $b=\frac{1}{3}$ thus period = $\dfrac{2\pi}{\frac{1}{3}}=6\pi$ amplitude = $|1| = 1$ To graph the function, perform the following steps: (1) With a period of $6\pi$, one period of the function is over the interval $[0, 6\pi]$. (2) Divide this interval into four parts to obtain the x-values $0, \frac{3}{2}\pi, 3\pi, \frac{9}{2}\pi, \text{ and } 6\pi$. (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 $[6\pi, 12\pi]$. (Refer to the graph in the answer part above.)

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