Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN: 9780134217437
Author: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher: PEARSON
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for the following graph listed. Amplitude in state the equation for the graph in both of the following forms

For the following graph, list the period and amplitude, and state the equation for the graph in both of the following forms: 1. **Period:** \[ \frac{\pi}{3} \] 2. **Amplitude:** \[ 2 \] ### Equations: (a) **Equation as a sine function:** \[ y = A \sin Bx \] (b) **Equation as a cosine function:** \[ y = A \cos Bx \] ### Graph Explanation The graph displays a trigonometric wave (sine or cosine) with the following characteristics: - **Amplitude:** The peak of the wave reaches 2 units from the horizontal axis. - **Period:** The wave completes one full cycle from \(-\pi\) to \(+\pi\), equivalent to a period of \(\frac{\pi}{3}\). The horizontal x-axis intersects the wave at intervals labeled in increments of \(\frac{\pi}{3}\). The vertical y-axis marks the amplitude, extending from -2 to 2.
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Transcribed Image Text:For the following graph, list the period and amplitude, and state the equation for the graph in both of the following forms: 1. **Period:** \[ \frac{\pi}{3} \] 2. **Amplitude:** \[ 2 \] ### Equations: (a) **Equation as a sine function:** \[ y = A \sin Bx \] (b) **Equation as a cosine function:** \[ y = A \cos Bx \] ### Graph Explanation The graph displays a trigonometric wave (sine or cosine) with the following characteristics: - **Amplitude:** The peak of the wave reaches 2 units from the horizontal axis. - **Period:** The wave completes one full cycle from \(-\pi\) to \(+\pi\), equivalent to a period of \(\frac{\pi}{3}\). The horizontal x-axis intersects the wave at intervals labeled in increments of \(\frac{\pi}{3}\). The vertical y-axis marks the amplitude, extending from -2 to 2.
Expert Solution
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Step 1: Define the problem

The standard equation of cosine and sine function 

rightwards double arrow f open parentheses x close parentheses equals A cos open parentheses B open parentheses x minus C close parentheses close parentheses plus D rightwards double arrow f open parentheses x close parentheses equals A sin open parentheses B open parentheses x minus C close parentheses close parentheses plus D

rightwards double arrow open vertical bar A close vertical bar equalsAmplitude 

rightwards double arrow T equals fraction numerator 2 straight pi over denominator B end fraction comma T equalstime period 

rightwards double arrow C equalsphase shift 

rightwards double arrow D equalsvertical shift 


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