Y= ____ (_____)(sin or cos) (______ x)

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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42. Y= ____ (_____)(sin or cos) (______ x)
The image shows a graph of a sinusoidal function, likely a trigonometric sine or cosine function, plotted on a Cartesian coordinate system. The x-axis is labeled with angles in radians, running from 0 to \(2\pi\), with marked points at \(\pi/2\), \(\pi\), \(3\pi/2\), and \(2\pi\). The y-axis ranges from -3 to 3.

### Description of the Graph:

- **Function Shape**: The function appears as a smooth curve that oscillates above and below the x-axis, indicative of a sine or cosine wave.
- **Peaks and Troughs**: The curve reaches positive peaks at approximately \(y = 3\) and negative troughs at \(y = -3\).
- **Intercepts**: The function crosses the x-axis at 0, \(\pi\), and \(2\pi\).
- **Wave Periodicity**: The period of the wave (the horizontal length before the graph repeats a similar pattern) appears to be \(2\pi\).

This graph helps in understanding the periodic nature of trigonometric functions and their applications in various fields such as physics, engineering, and signal processing.
Transcribed Image Text:The image shows a graph of a sinusoidal function, likely a trigonometric sine or cosine function, plotted on a Cartesian coordinate system. The x-axis is labeled with angles in radians, running from 0 to \(2\pi\), with marked points at \(\pi/2\), \(\pi\), \(3\pi/2\), and \(2\pi\). The y-axis ranges from -3 to 3. ### Description of the Graph: - **Function Shape**: The function appears as a smooth curve that oscillates above and below the x-axis, indicative of a sine or cosine wave. - **Peaks and Troughs**: The curve reaches positive peaks at approximately \(y = 3\) and negative troughs at \(y = -3\). - **Intercepts**: The function crosses the x-axis at 0, \(\pi\), and \(2\pi\). - **Wave Periodicity**: The period of the wave (the horizontal length before the graph repeats a similar pattern) appears to be \(2\pi\). This graph helps in understanding the periodic nature of trigonometric functions and their applications in various fields such as physics, engineering, and signal processing.
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