This educational example involves matching trigonometric functions to their respective graphs. The functions provided are cosecant, tangent, secant, and cotangent. The goal is to identify which graph represents each function.1. **Graph Overview:** - **Graph 1:** Blue curves with vertical asymptotes at \(x = -3\pi/2\), \(-\pi/2\), \(\pi/2\), \(3\pi/2\). The graph spans upwards and downwards between these asymptotes, indicating a periodicity and asymmetry typical of cotangent or cosecant functions. 2. **Graph 2:** Features similar blue arcs and red dashed asymptotes with a distinct repeating pattern. The curves are symmetric about certain points, indicating this might represent the secant or tangent function. Noticeable asymptotes are seen at \(x = -2\pi\), \(0\), \(\pi\), \(2\pi\).3. **Graph 3:** Similar in style to graph 1, but inverted with asymptotes at similar intervals. This graph is potentially representing a cotangent or secant function due to its pattern and placements.4. **Graph 4:** Contains oscillating curves with vertical asymptotes at \(-3\pi/2\), \(-\pi/2\), \(\pi/2\), \(3\pi/2\). This style suggests a cosecant or cotangent function because of its periodic features and symmetry.**Graphs Interpretation:**- Functions like cosecant and secant have characteristics where the graph includes vertical asymptotes and does not intersect the x-axis, fitting the pattern of U-shaped curves.- The tangent and cotangent functions also feature asymptotes, however, they intersect the x-axis and create a pattern repeating every \(\pi\) or localized segments between \(-\pi\) and \(\pi\).To identify correctly, review attributes of trigonometric functions:- **Cosecant \( \csc x \):** Reciprocal of sine; undefined where sine is zero, creating vertical asymptotes.- **Secant \( \sec x \):** Reciprocal of cosine; undefined where cosine is zero, with vertical asymptotes.- **Tangent \( \tan x \):** Slope of sine and cosine, with asymptotes where cosine is zero.- **Cotangent \(

Name: This educational example involves matching trigonometric functions to
Uploaded: 2024-03-20T06:46:55.000Z
Channel: Bartleby
Description: This educational example involves matching trigonometric functions to their respective graphs. The functions provided are cosecant, tangent, secant, and cotangent. The goal is to identify which graph represents each function.1. **Graph Overview:**