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y = tanx 12 **

y = tanx 12 **

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Graph please
**Transcription and Explanation for Educational Website:** --- **1. \( y = \tan x \)** **Graph Description:** The graph represents the function \( y = \tan x \), or the tangent function. This function is periodic with a period of \( \pi \). The graph is characterized by the following features: - **Asymptotes:** Vertical asymptotes appear where the function is undefined, specifically at \( x = \frac{\pi}{2} + n\pi \) for any integer \( n \). This occurs because the tangent function approaches infinity as it nears these x-values. - **Intercepts:** The function crosses the x-axis at integer multiples of \( \pi \), i.e., \( x = n\pi \). - **Behavior between Asymptotes:** Between each pair of consecutive asymptotes, the tangent function crosses the x-axis and increases from negative infinity to positive infinity. - **Periodicity:** Every section of the graph repeats itself every \( \pi \) units along the x-axis. This graph visually demonstrates the undefined behavior at the vertical asymptotes and the periodic nature of the tangent function. The tangent function is often used in trigonometry to relate angles to ratios in right triangles and has applications in various fields such as physics and engineering. --- This explanation covers the essential characteristics of the \( \tan x \) graph in a visual format.
Transcribed Image Text:**Transcription and Explanation for Educational Website:** --- **1. \( y = \tan x \)** **Graph Description:** The graph represents the function \( y = \tan x \), or the tangent function. This function is periodic with a period of \( \pi \). The graph is characterized by the following features: - **Asymptotes:** Vertical asymptotes appear where the function is undefined, specifically at \( x = \frac{\pi}{2} + n\pi \) for any integer \( n \). This occurs because the tangent function approaches infinity as it nears these x-values. - **Intercepts:** The function crosses the x-axis at integer multiples of \( \pi \), i.e., \( x = n\pi \). - **Behavior between Asymptotes:** Between each pair of consecutive asymptotes, the tangent function crosses the x-axis and increases from negative infinity to positive infinity. - **Periodicity:** Every section of the graph repeats itself every \( \pi \) units along the x-axis. This graph visually demonstrates the undefined behavior at the vertical asymptotes and the periodic nature of the tangent function. The tangent function is often used in trigonometry to relate angles to ratios in right triangles and has applications in various fields such as physics and engineering. --- This explanation covers the essential characteristics of the \( \tan x \) graph in a visual format.
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