**Graphing Trigonometric Functions****Problem 7: Graph the function** \[ y = -3 \csc(\pi \theta) \]**Instructions:**- We are tasked with graphing the trigonometric function \(-3 \csc(\pi \theta)\). - To begin, recognize that the cosecant function, \(\csc(x)\), is the reciprocal of the sine function.- The graph of \(\csc(x)\) will have vertical asymptotes where the function is undefined, which occurs at the zeros of \(\sin(x)\).**Graph Details:**- The grid provided is a rectangular coordinate system.- The horizontal axis typically represents values of \(\theta\), while the vertical axis represents values of \(y\).- Make note of key \( \theta \) values where the cosecant function has asymptotes and peaks.**Approach:**1. **Identify Asymptotes:** Due to the factor of \(\pi \theta\) in the argument, the function is undefined where \(\sin(\pi \theta) = 0\). This occurs at integer values of \(\theta\).2. **Amplitudes and Periods:** The amplitude of the function is affected by the coefficient \(-3\), which stretches the graph vertically and reflects it across the horizontal axis. The period is determined by the factor of \(\pi\) and is \(2\).3. **Sketch Points:** Plot points where the function has defined values, considering the negative and amplified aspect due to \(-3\).4. **Draw the Graph:** Include the curves that approach the asymptotes but never touch. The graph should reflect the transformation of the parent \(\csc\) function.Ensure to label any asymptotes and key points to aid in comprehending the transformations applied to the basic cosecant function.

Name: **Graphing Trigonometric Functions****Problem 7: Graph the function**
Uploaded: 2024-03-20T06:47:22.000Z
Channel: Bartleby
Description: **Graphing Trigonometric Functions****Problem 7: Graph the function** \[ y = -3 \csc(\pi \theta) \]**Instructions:**- We are tasked with graphing the trigonometric function \(-3 \csc(\pi \theta)\). - To begin, recognize that the cosecant function, \