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Determine the period of the following graph. 2 1

Determine the period of the following graph. 2 1

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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## Determine the Period of the Following Graph To determine the period of a trigonometric graph, you need to identify the length of one complete cycle of the graph along the x-axis. ### Analysis of the Graph The graph provided is a sinusoidal wave. The y-axis ranges from -5 to 5, and the x-axis is marked from -2π to 3π, with increments of π/2. ### Observations 1. The graph starts at -2π on the left, reaches a minimum at -π, goes to a maximum at π, and then continues the pattern. 2. The starting point of the graph (peaks/valleys) repeats after a specific interval along the x-axis. ### Determining the Period - From minimum at -π to maximum at π, we cover one complete cycle, as the pattern repeats itself after π/2 to 2π interval. - The period here is thus the distance between two repeating points along the x-axis. **Conclusion:** The period of this sinusoidal graph is 2π. Note: Always ensure to compare the graph's repeating cycles to properly confirm the periodic interval. ### Graph Summary - **Axis Labels:** - x-axis ranges from -2π to 3π. - y-axis ranges from -5 to 5. - **Periodic Nature:** - The pattern reiterates every 2π units along the x-axis. Understanding the period helps comprehend the behavior of trigonometric functions, which is essential in various applications in mathematics, physics, and engineering.
Transcribed Image Text:## Determine the Period of the Following Graph To determine the period of a trigonometric graph, you need to identify the length of one complete cycle of the graph along the x-axis. ### Analysis of the Graph The graph provided is a sinusoidal wave. The y-axis ranges from -5 to 5, and the x-axis is marked from -2π to 3π, with increments of π/2. ### Observations 1. The graph starts at -2π on the left, reaches a minimum at -π, goes to a maximum at π, and then continues the pattern. 2. The starting point of the graph (peaks/valleys) repeats after a specific interval along the x-axis. ### Determining the Period - From minimum at -π to maximum at π, we cover one complete cycle, as the pattern repeats itself after π/2 to 2π interval. - The period here is thus the distance between two repeating points along the x-axis. **Conclusion:** The period of this sinusoidal graph is 2π. Note: Always ensure to compare the graph's repeating cycles to properly confirm the periodic interval. ### Graph Summary - **Axis Labels:** - x-axis ranges from -2π to 3π. - y-axis ranges from -5 to 5. - **Periodic Nature:** - The pattern reiterates every 2π units along the x-axis. Understanding the period helps comprehend the behavior of trigonometric functions, which is essential in various applications in mathematics, physics, and engineering.
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