we have the function
[tex]E=\sin \frac{\pi}{14}t[/tex]
Part a
For t=7
substitute in the given function
[tex]\begin{gathered} E=\sin \frac{\pi}{14}7 \\ E=1 \end{gathered}[/tex]
For t=14
[tex]\begin{gathered} E=\sin \frac{\pi}{14}14 \\ E=0 \end{gathered}[/tex]
For t=21
[tex]\begin{gathered} E=\sin \frac{\pi}{14}21 \\ E=-1 \end{gathered}[/tex]
For t=28
[tex]\begin{gathered} E=\sin \frac{\pi}{14}28 \\ E=0 \end{gathered}[/tex]
For t=35
[tex]\begin{gathered} E=\sin \frac{\pi}{14}35 \\ E=1 \end{gathered}[/tex]
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
