Find the amplltude, period, and phase shift of the function. cos(x + =) amplitude period phase shift Graph one complete period. y y 3 3
Find the amplltude, period, and phase shift of the function. cos(x + =) amplitude period phase shift Graph one complete period. y y 3 3
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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![The problem presented is to find the amplitude, period, and phase shift of the cosine function given by:
\[ y = 3 \cos \left( x + \frac{\pi}{6} \right) \]
There are boxes indicating where to fill in the values for:
- Amplitude
- Period
- Phase Shift
Below the problem statement, there is a section titled "Graph one complete period" with four different graphs illustrating the function:
1. **First Graph**:
- The x-axis is labeled from \(-\pi\) to \(2\pi\) with intermediate markings at \(-\frac{2\pi}{3}\), \(\frac{\pi}{3}\), \(\pi\), and \(\frac{4\pi}{3}\).
- The y-axis is labeled from \(-3\) to \(3\).
- The graph is a cosine wave starting at the negative x-axis, peaking at \(y = 3\) near \(\frac{\pi}{3}\), and returning to \(0\) at \(2\pi\).
2. **Second Graph**:
- Same axis labels as the first graph.
- The cosine wave starts closer to the x-axis, dips to \(y = -3\) around \(\frac{2\pi}{3}\), and returns to \(0\) near \(2\pi\).
3. **Third Graph**:
- The x-axis is labeled from \(-\pi\) to \(2\pi\) with intermediate markings at \(-\pi\), \(0\), \(\frac{5\pi}{6}\), and \(\frac{11\pi}{6}\).
- The cosine wave begins near \(-\pi\), reaches a peak at \(y = 3\) around \(\frac{5\pi}{6}\), and returns to \(0\) near \(\frac{11\pi}{6}\).
4. **Fourth Graph**:
- The x-axis labels are similar to the third graph.
- The wave starts further along the positive x-axis, reaching a trough at \(y = -3\) near \(\frac{5\pi}{6}\), and returning towards \(0\) after \(\frac{11\pi}{6}\).
These graphs illustrate how the amplitude, phase shift, and period affect](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F725e19a4-aaf6-4615-a1c3-c5095a83cc37%2F4a705c92-0424-48cd-9d85-5f53e165c65f%2Fn9r5l7g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The problem presented is to find the amplitude, period, and phase shift of the cosine function given by:
\[ y = 3 \cos \left( x + \frac{\pi}{6} \right) \]
There are boxes indicating where to fill in the values for:
- Amplitude
- Period
- Phase Shift
Below the problem statement, there is a section titled "Graph one complete period" with four different graphs illustrating the function:
1. **First Graph**:
- The x-axis is labeled from \(-\pi\) to \(2\pi\) with intermediate markings at \(-\frac{2\pi}{3}\), \(\frac{\pi}{3}\), \(\pi\), and \(\frac{4\pi}{3}\).
- The y-axis is labeled from \(-3\) to \(3\).
- The graph is a cosine wave starting at the negative x-axis, peaking at \(y = 3\) near \(\frac{\pi}{3}\), and returning to \(0\) at \(2\pi\).
2. **Second Graph**:
- Same axis labels as the first graph.
- The cosine wave starts closer to the x-axis, dips to \(y = -3\) around \(\frac{2\pi}{3}\), and returns to \(0\) near \(2\pi\).
3. **Third Graph**:
- The x-axis is labeled from \(-\pi\) to \(2\pi\) with intermediate markings at \(-\pi\), \(0\), \(\frac{5\pi}{6}\), and \(\frac{11\pi}{6}\).
- The cosine wave begins near \(-\pi\), reaches a peak at \(y = 3\) around \(\frac{5\pi}{6}\), and returns to \(0\) near \(\frac{11\pi}{6}\).
4. **Fourth Graph**:
- The x-axis labels are similar to the third graph.
- The wave starts further along the positive x-axis, reaching a trough at \(y = -3\) near \(\frac{5\pi}{6}\), and returning towards \(0\) after \(\frac{11\pi}{6}\).
These graphs illustrate how the amplitude, phase shift, and period affect
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