10. Find a possible formula y = A cos(Bx) + C for the graph: -2 --6- -8 y
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 10:** Find a possible formula \( y = A \cos(Bx) + C \) for the graph.
**Graph Explanation:**
The given graph is a cosine wave plotted on a coordinate plane. Let's break down the components:
- **Amplitude (A):** The vertical distance from the centerline to the peak of the wave. Here, the maximum value is 4 and the minimum value is -4, giving an amplitude of \( A = 4 \).
- **Vertical Shift (C):** The centerline of the wave is y = 0, indicating no vertical shift. Thus, \( C = 0 \).
- **Period (T):** The length of one complete cycle of the wave. The wave completes a cycle from x = 0 to x = 2, giving a period of 2. The formula for the period of a cosine wave is \( T = \frac{2\pi}{B} \). Therefore, \( B = \frac{2\pi}{2} = \pi \).
Based on this analysis, the possible formula for the graph is:
\[ y = 4 \cos(\pi x) \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F797abc1e-1910-4437-94e2-bed043a24819%2Fd3e3a97d-3855-415c-9c77-4e9407dc2b9f%2F9vpsa3ca_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 10:** Find a possible formula \( y = A \cos(Bx) + C \) for the graph.
**Graph Explanation:**
The given graph is a cosine wave plotted on a coordinate plane. Let's break down the components:
- **Amplitude (A):** The vertical distance from the centerline to the peak of the wave. Here, the maximum value is 4 and the minimum value is -4, giving an amplitude of \( A = 4 \).
- **Vertical Shift (C):** The centerline of the wave is y = 0, indicating no vertical shift. Thus, \( C = 0 \).
- **Period (T):** The length of one complete cycle of the wave. The wave completes a cycle from x = 0 to x = 2, giving a period of 2. The formula for the period of a cosine wave is \( T = \frac{2\pi}{B} \). Therefore, \( B = \frac{2\pi}{2} = \pi \).
Based on this analysis, the possible formula for the graph is:
\[ y = 4 \cos(\pi x) \]
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