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Graph the function y = - 4 sin Give the period and the amplitude. .... Choose the correct graph of the function. O A. В. Oc. D. Ay 5- y 5- Ay 5- 8x

Graph the function y = - 4 sin Give the period and the amplitude. .... Choose the correct graph of the function. O A. В. Oc. D. Ay 5- y 5- Ay 5- 8x

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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Question

Graph, give the period, and find the amplitude.

Graph the function \( y = -4 \sin \left( \frac{1}{4} x \right) \). Give the period and the amplitude. **Choose the correct graph of the function.** - **Option A**: The graph is shown with an amplitude of 4, starting at the origin, reaching a maximum of -4, crossing the x-axis at \(4\pi\), and completing a full cycle at \(8\pi\). - **Option B**: The graph is shown with an amplitude of 4, starting at the origin, reaching a maximum of 4, crossing the x-axis at \(4\pi\), and completing a full cycle at \(8\pi\). - **Option C**: The graph is shown inverted with an amplitude of 4, starting at 0, reaching a minimum of -4, crossing the x-axis at \(4\pi\), and completing a full cycle at \(8\pi\). - **Option D**: The graph is shown with an amplitude of 4, starting at 0, reaching a maximum of 4, and oscillating with a full cycle repeating. **Explanation of the Function and Graph:** 1. **Amplitude**: The amplitude of the function is 4, as indicated by the coefficient of the sine function. 2. **Period**: The period \( T \) can be calculated using the formula \( T = \frac{2\pi}{b} \), where \( b \) is the frequency. Here, \( b = \frac{1}{4} \), so \( T = 8\pi \). The correct graph reflects these properties, showing the negative amplitude and the period of \( 8\pi \). Thus, Option C correctly represents the function.
Transcribed Image Text:Graph the function \( y = -4 \sin \left( \frac{1}{4} x \right) \). Give the period and the amplitude. **Choose the correct graph of the function.** - **Option A**: The graph is shown with an amplitude of 4, starting at the origin, reaching a maximum of -4, crossing the x-axis at \(4\pi\), and completing a full cycle at \(8\pi\). - **Option B**: The graph is shown with an amplitude of 4, starting at the origin, reaching a maximum of 4, crossing the x-axis at \(4\pi\), and completing a full cycle at \(8\pi\). - **Option C**: The graph is shown inverted with an amplitude of 4, starting at 0, reaching a minimum of -4, crossing the x-axis at \(4\pi\), and completing a full cycle at \(8\pi\). - **Option D**: The graph is shown with an amplitude of 4, starting at 0, reaching a maximum of 4, and oscillating with a full cycle repeating. **Explanation of the Function and Graph:** 1. **Amplitude**: The amplitude of the function is 4, as indicated by the coefficient of the sine function. 2. **Period**: The period \( T \) can be calculated using the formula \( T = \frac{2\pi}{b} \), where \( b \) is the frequency. Here, \( b = \frac{1}{4} \), so \( T = 8\pi \). The correct graph reflects these properties, showing the negative amplitude and the period of \( 8\pi \). Thus, Option C correctly represents the function.
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