graph the trigonometric function. then give the xmin and xmax values for the viewing window xmin, xmax by…

Explanation:

Step1: Recall period formula for $y = \csc(bx)$

The period of $y=\csc(bx)$ is $\frac{2\pi}{|b|}$. For $y = \csc(4x)$, $b = 4$, so the period is $\frac{2\pi}{4}=\frac{\pi}{2}$.

Step2: Determine viewing - window for one period

We want to show one full - period of the function $y=\csc(4x)$ in the $x$ - direction. A common choice for the period of the cosecant function is from $0$ to $\frac{\pi}{2}$. So, $X_{min}=0$ and $X_{max}=\frac{\pi}{2}$. The graph of $y = \csc(4x)$ has vertical asymptotes at $4x = k\pi$, where $k\in\mathbb{Z}$, or $x=\frac{k\pi}{4}$, and it has the same general shape as the basic cosecant function but is compressed horizontally by a factor of $\frac{1}{4}$.

Answer:

B. $[0,\frac{\pi}{2}]$ by $[- 10,10]$