Explanation:
The general template of a sine function is
y = Asin(B(x-C))+D
The value of B is the only thing that determines the period T. We ignore every other term.
It turns out that T = 2pi/B which can be solved to B = 2pi/T
Plug in the given period of T = 8pi and compute to get
B = 2pi/T
B = (2pi)/(8pi)
B = 2/8
B = 1/4
This means that the term out front of the x is 1/4 and the equation must be [tex]y = \sin\left(\frac{1}{4}x\right)[/tex] which matches with answer choice B.
