Question

graph the following function over a two - period interval. give the period and the amplitude. y = sin 3x the period of the function y = sin 3x is . (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall sine - function period formula

For the function $y = A\sin(Bx - C)+D$, the period $T$ is given by $T=\frac{2\pi}{|B|}$. In the function $y=\sin(3x)$, $B = 3$.

Step2: Calculate the period

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

Answer:

$\frac{2\pi}{3}$