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

Given the function below

`y=2\cos(\pi)/(3)\theta`

Applying the general cosine function formula

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

The amplitude is

`a=2`

The period is

`\begin{gathered} Period=(2\pi)/(b) \\ b=(\pi)/(3) \\ Period=(2\pi)/((\pi)/(3))=2\pi*(3)/(\pi)=2*3=6 \end{gathered}`

Hence, the period is 6 and amplitude is 2

The graph of the function is shown below