#### Answer

a. $E(7)= 1$, $E(14)= 0$, $E(21) =-1$, $E(28)= 0$, $E(35)= 1$, oscillates in the interval of $[-1,1]$.
b. $28\ days$

#### Work Step by Step

a. With the given function $E(t)=sin(\frac{\pi}{14}t)$, we have $E(7)=sin(\frac{\pi}{2})=1$, $E(14)=sin(\pi)=0$, $E(21)=sin(\frac{3\pi}{2})=-1$, $E(28)=sin(2\pi)=0$, $E(35)=sin(\frac{5\pi}{2})=1$
We can see that the function oscillates in the interval of $[-1,1]$.
b. The period of the cycle can be found as $p=\frac{2\pi}{\pi/14}=28\ days$ as can be observed from $E(7)$ to $E(35)$ above.