Graph two periods of the given cosecant or secant function.


y = 2 csc x

Verified step by step guidance

1. Identify the basic function: The given function is $y=2\csc x$, which is a transformation of the cosecant function $\csc x=\frac{1}{\sin x}$.
2. Determine the period: The period of $\csc x$ is $2\pi$. Since there is no horizontal stretch or compression, the period of $y=2\csc x$ remains $2\pi$.
3. Identify the vertical stretch: The coefficient 2 indicates a vertical stretch by a factor of 2. This means the maximum and minimum values of the cosecant function will be multiplied by 2.
4. Locate the vertical asymptotes: The vertical asymptotes of $\csc x$ occur where $\sin x=0$, which is at $x=n\pi$ for integer $n$. These will remain the same for $y=2\csc x$.
5. Graph two periods: Plot the function over the interval $[0,4\pi ]$, marking the vertical asymptotes at $x=0,\pi ,2\pi ,3\pi ,4\pi$, and sketch the curves of $y=2\csc x$ between these asymptotes, showing the vertical stretch.