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Write the equation of the trigonometric graph. 4 2. 1. -27 -37 元 37 2元 3T 9元 15元 117 16元 2 2 12 2. -1 -2 -3 -4 -5

Write the equation of the trigonometric graph. 4 2. 1. -27 -37 元 37 2元 3T 9元 15元 117 16元 2 2 12 2. -1 -2 -3 -4 -5

Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Write the equation of the trigonometric graph
**Title: Understanding Trigonometric Graphs** --- **Instruction: Write the equation of the trigonometric graph.** --- **Detailed Analysis of the Graph:** The graph provided is a trigonometric function with the following detailed characteristics: 1. **Axes Information:** - The horizontal axis is labeled as \( x \). - The vertical axis is labeled as \( y \). 2. **Grid and Scale:** - The grid lines on the graph help to understand the scale and periodicity of the function. - The \( x \)-axis has critical points marked at intervals of \(\frac{\pi}{2}\) ranging from \(-2\pi\) to \(6\pi\). Specifically, notable points include \(-2\pi\), \(-\frac{3\pi}{2}\), \(-\pi\), \(-\frac{\pi}{2}\), \(0\), \(\frac{\pi}{2}\), \(\pi\), \(\frac{3\pi}{2}\), \(2\pi\), \( \frac{5\pi}{2}\), \(3\pi\), \(\frac{7\pi}{2}\), \(4\pi\), \(\frac{9\pi}{2}\), \(5\pi\), \(\frac{11\pi}{2}\), and \(6\pi\). 3. **Wave Characteristics:** - The graph represents a periodic wave. - From observation, each complete cycle spans a distance of \(2\pi\) units along the \( x \)-axis. - The amplitude (maximum |y| value reached) of the wave is 1, which is observed from the peak and trough values at \(1\) and \(-1\) respectively. - The graph consistently crosses the \( x \)-axis at multiples of \( \pi\) (i.e., \(-2\pi\), \(-\pi\), \(0\), \(\pi\), \(2\pi\), \(3\pi\), etc.) 4. **Type of Trigonometric Function:** - The wave appears sinusoidal in nature, suggesting it may either be a sine or cosine function. - Given it crosses the origin \( (0,0) \), this indicates the function is likely a sine function (since \(\sin(0)
Transcribed Image Text:**Title: Understanding Trigonometric Graphs** --- **Instruction: Write the equation of the trigonometric graph.** --- **Detailed Analysis of the Graph:** The graph provided is a trigonometric function with the following detailed characteristics: 1. **Axes Information:** - The horizontal axis is labeled as \( x \). - The vertical axis is labeled as \( y \). 2. **Grid and Scale:** - The grid lines on the graph help to understand the scale and periodicity of the function. - The \( x \)-axis has critical points marked at intervals of \(\frac{\pi}{2}\) ranging from \(-2\pi\) to \(6\pi\). Specifically, notable points include \(-2\pi\), \(-\frac{3\pi}{2}\), \(-\pi\), \(-\frac{\pi}{2}\), \(0\), \(\frac{\pi}{2}\), \(\pi\), \(\frac{3\pi}{2}\), \(2\pi\), \( \frac{5\pi}{2}\), \(3\pi\), \(\frac{7\pi}{2}\), \(4\pi\), \(\frac{9\pi}{2}\), \(5\pi\), \(\frac{11\pi}{2}\), and \(6\pi\). 3. **Wave Characteristics:** - The graph represents a periodic wave. - From observation, each complete cycle spans a distance of \(2\pi\) units along the \( x \)-axis. - The amplitude (maximum |y| value reached) of the wave is 1, which is observed from the peak and trough values at \(1\) and \(-1\) respectively. - The graph consistently crosses the \( x \)-axis at multiples of \( \pi\) (i.e., \(-2\pi\), \(-\pi\), \(0\), \(\pi\), \(2\pi\), \(3\pi\), etc.) 4. **Type of Trigonometric Function:** - The wave appears sinusoidal in nature, suggesting it may either be a sine or cosine function. - Given it crosses the origin \( (0,0) \), this indicates the function is likely a sine function (since \(\sin(0)
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