the period is 8
Explanation
the function sin has the form
[tex]\begin{gathered} y=Asin(B(x+c))+D \\ where \\ Period=\frac{2\pi}{B} \end{gathered}[/tex]
so
Step 1
a) identify B in the given function
given
[tex]d=5\text{ sin\lparen}\frac{\pi}{4}t)[/tex]
hence
[tex]\begin{gathered} \frac{\pi}{4}t\Rightarrow B(t+c) \\ so \\ c=0 \\ \frac{\pi}{4}t=Bt \\ therefore \\ B=\frac{\pi}{4} \end{gathered}[/tex]
b) now, replace in the formula to find teh period
[tex]\begin{gathered} Per\imaginaryI od=\frac{2\pi}{B} \\ Period=\frac{2\pi}{\frac{\pi}{4}}=\frac{2\pi *4}{1*\pi}=\frac{8\pi}{\pi}=8 \\ so \\ Period=8 \end{gathered}[/tex]
therefore, the period is 8
I hope this helps you
