Sketch the graph of the function g(x) = 3cos(2x) on the interval -2n s x s 2n.

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°.
icon
Related questions
icon
Concept explainers
Topic Video
Question

thank youu!!

**Sketch the Graph of the Function \( y(x) = 3 \cos(2x) \) on the Interval \(-2\pi \leq x \leq 2\pi\)**

The graph of the function \( y(x) = 3 \cos(2x) \) is to be sketched over the interval \(-2\pi \leq x \leq 2\pi\). 

### Description of the Graph:

- **Axes**: The graph is plotted on a Cartesian coordinate system with the x-axis representing the variable \( x \) and the y-axis representing the function \( y(x) \).
  
- **X-Axis Range**: The x-axis ranges from \(-2\pi\) to \(2\pi\). Notable points on the x-axis include:
  - \(-2\pi\)
  - \(-\pi\)
  - \(0\)
  - \(\pi\)
  - \(2\pi\)

- **Y-Axis Range**: The y-axis has values marked from -5 to 5.

- **Amplitude**: The function \( y(x) = 3 \cos(2x) \) has an amplitude of 3, meaning the graph will oscillate between 3 and -3 on the y-axis.

- **Frequency**: The function inside the cosine, \( 2x \), causes the graph to complete 2 cycles within the interval \(-\pi \) to \(\pi\). Therefore, within \(-2\pi\) to \(2\pi\), the graph will complete 4 cycles.

### Key Points of the Function \( y(x) = 3 \cos(2x) \):

1. **Maximum points** occur at \( x = -2\pi, -\pi, 0, \pi, 2\pi \) where \( y = 3 \).
2. **Minimum points** occur at \( x = -3\pi/2, -\pi/2, \pi/2, 3\pi/2 \) where \( y = -3 \).
3. **Zero points** occur at \( x = -\pi/2, \pi/2, 3\pi/2, ... \) where \( y = 0 \).

### Appearance of the Graph:

- The graph will have periodic
Transcribed Image Text:**Sketch the Graph of the Function \( y(x) = 3 \cos(2x) \) on the Interval \(-2\pi \leq x \leq 2\pi\)** The graph of the function \( y(x) = 3 \cos(2x) \) is to be sketched over the interval \(-2\pi \leq x \leq 2\pi\). ### Description of the Graph: - **Axes**: The graph is plotted on a Cartesian coordinate system with the x-axis representing the variable \( x \) and the y-axis representing the function \( y(x) \). - **X-Axis Range**: The x-axis ranges from \(-2\pi\) to \(2\pi\). Notable points on the x-axis include: - \(-2\pi\) - \(-\pi\) - \(0\) - \(\pi\) - \(2\pi\) - **Y-Axis Range**: The y-axis has values marked from -5 to 5. - **Amplitude**: The function \( y(x) = 3 \cos(2x) \) has an amplitude of 3, meaning the graph will oscillate between 3 and -3 on the y-axis. - **Frequency**: The function inside the cosine, \( 2x \), causes the graph to complete 2 cycles within the interval \(-\pi \) to \(\pi\). Therefore, within \(-2\pi\) to \(2\pi\), the graph will complete 4 cycles. ### Key Points of the Function \( y(x) = 3 \cos(2x) \): 1. **Maximum points** occur at \( x = -2\pi, -\pi, 0, \pi, 2\pi \) where \( y = 3 \). 2. **Minimum points** occur at \( x = -3\pi/2, -\pi/2, \pi/2, 3\pi/2 \) where \( y = -3 \). 3. **Zero points** occur at \( x = -\pi/2, \pi/2, 3\pi/2, ... \) where \( y = 0 \). ### Appearance of the Graph: - The graph will have periodic
Expert Solution
steps

Step by step

Solved in 2 steps with 3 images

Blurred answer
Knowledge Booster
Sample space, Events, and Basic Rules of Probability
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Trigonometry (11th Edition)
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Algebra and Trigonometry
Algebra and Trigonometry
Trigonometry
ISBN:
9781938168376
Author:
Jay Abramson
Publisher:
OpenStax
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning