Question

question 12 of 25
what is the period of the graph of ( y = 5 sin ( 4 pi x ) + 3 )?
a. ( 4 pi )
b. 3
c. ( \frac { 1 } { 2 } )
d. 5

Explanation:

Step1: Recall sine function period formula

For $y = A\sin(Bx + C) + D$, period is $\frac{2\pi}{|B|}$.

Step2: Identify B in the given function

Given $y = 5\sin(4\pi x) + 3$, so $B = 4\pi$.

Step3: Calculate the period

Substitute B into formula: $\frac{2\pi}{4\pi} = \frac{1}{2}$.

Answer:

C. $\frac{1}{2}$