Question

what is the period of the graph of ( y = 5 sin(4pi x)+3 )?

a ( 4pi )
b. 5
c. 3
d. ( \frac{1}{2} )

Explanation:

Step1: Recall the formula for the period of a sine function

The general form of a sine function is \(y = A\sin(Bx - C)+D\), and its period is given by \(T=\frac{2\pi}{|B|}\).

Step2: Identify the value of \(B\) in the given function

For the function \(y = 5\sin(4\pi x)+3\), we have \(B = 4\pi\).

Step3: Calculate the period

Substitute \(B = 4\pi\) into the period formula \(T=\frac{2\pi}{|B|}\). So \(T=\frac{2\pi}{4\pi}\).
Simplify \(\frac{2\pi}{4\pi}=\frac{1}{2}\).

Answer:

D. \(\frac{1}{2}\)