Question

find the amplitude (if one exists), period, and phase shift of the function. graph the function. be sure to label key points. show at least two periods.
y = 5 sin(3x - π)
what is the amplitude? select the correct choice and, if necessary, fill in the answer box to complete your choice
a. the amplitude is 5
(simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.)
b. the function does not have an amplitude
what is the period?
(simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression )

Explanation:

Step1: Recall period formula for sine function

The general form of a sine - function is $y = A\sin(Bx - C)+D$. The period $T$ of the sine function $y = A\sin(Bx - C)+D$ is given by $T=\frac{2\pi}{|B|}$.
For the function $y = 5\sin(3x-\pi)$, we have $B = 3$.

Step2: Calculate the period

Substitute $B = 3$ into the period formula $T=\frac{2\pi}{|B|}$.
Since $|B|=|3| = 3$, then $T=\frac{2\pi}{3}$.

Answer:

The period is $\frac{2\pi}{3}$