drag the slider to change the value of b and observe the effect of b on the graph of the sine function. when…

Explanation:

Step1: Recall period formula

The period formula for the sine - function $y = A\sin(bx)$ is $T=\frac{2\pi}{|b|}$.

Step2: Calculate period when $b = 0.5$

Substitute $b = 0.5$ into the formula $T=\frac{2\pi}{|b|}$. Since $|b|=0.5$, then $T=\frac{2\pi}{0.5}=4\pi$.

Step3: Calculate period when $b = 2$

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

Answer:

When $b = 0.5$, the period is $4$; when $b = 2$, the period is $1$.