Question

Hello this is algebra 2 or geometry im looking for number 2 and the question includes finding the period and amplitude. The third part is to sketch one cycle of the graph of the function.

Answer 1

Solution:

Given the function below

$y=2\cos\frac{\pi}{3}\theta$

Applying the general cosine function formula

$\begin{gathered} y=a\cos(bx-c)+d \\ Where \\ a\text{ is the amplitude} \\ Period=\frac{2\pi}{b} \end{gathered}$

The amplitude is

$a=2$

The period is

$\begin{gathered} Period=\frac{2\pi}{b} \\ b=\frac{\pi}{3} \\ Period=\frac{2\pi}{\frac{\pi}{3}}=2\pi\times\frac{3}{\pi}=2\times3=6 \end{gathered}$

Hence, the period is 6 and amplitude is 2

The graph of the function is shown below