Question

Please see the image and help with this homework problem. thank you!

Answer 1

we have the function

$E=\sin \frac{\pi}{14}t$

Part a

For t=7

substitute in the given function

$\begin{gathered} E=\sin \frac{\pi}{14}7 \\ E=1 \end{gathered}$

For t=14

$\begin{gathered} E=\sin \frac{\pi}{14}14 \\ E=0 \end{gathered}$

For t=21

$\begin{gathered} E=\sin \frac{\pi}{14}21 \\ E=-1 \end{gathered}$

For t=28

$\begin{gathered} E=\sin \frac{\pi}{14}28 \\ E=0 \end{gathered}$

For t=35

$\begin{gathered} E=\sin \frac{\pi}{14}35 \\ E=1 \end{gathered}$

Observation: The values of E varies from -1 to 1, including the zero

Part B

Remember that

The Period goes from one peak to the next

so

Period=2pi/B

B=pi/14

Period=(2pi)/(pi/14)=2pi*14/pi=28

the period is 28 days