what is the period of the graph of y = 1/2 sin(2x) - 3?\na. 1/2\nb. π\nc. 3\nd. 2

Explanation:

Step1: Recall period formula for sine function

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

Step2: Identify the value of B

For the function $y=\frac{1}{2}\sin(2x)-3$, comparing it with $y = A\sin(Bx - C)+D$, we have $B = 2$.

Step3: Calculate the period

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

Answer:

B. $\pi$