## Trigonometry Exercise: Understanding Parametric Equations ### Problem Statement Given the parametric equations: - \( x = \cos(2t) \) - \( y = \cos(t) \) Fill in the table with the values of \( t \), \( x \), and \( y \), and plot the corresponding points on the graph. ### Table of Values | \( t \) | \( x = \cos(2t) \) | \( y = \cos(t) \) | \( (x, y) \) | |------------|--------------------|-------------------|---------------| | 0 | 1 | 1 | (1, 1) | | \( \pi/4 \)| 0 | \( \approx 0.7 \) | (0, 0.7) | | \( \pi/2 \)| | | | | \( 3\pi/4 \)| | | | | \( \pi \) | | | | | \( 5\pi/4 \)| | | | | \( 3\pi/2 \)| | | | | \( 7\pi/4 \)| | | | | \( 2\pi \) | | | | ### Graph Description The graph is a coordinate plane with axes labeled \( x \) and \( y \) ranging from -8 to 8. A single plotted point, corresponding to \( t = 0 \), \( (x, y) = (1, 1) \), is marked. The graph allows for plotting additional points derived from the completed table to visualize the relationship between \( x \) and \( y \) as \( t \) varies. **Instructions:** - Continue by calculating the other values for \( t \) and complete the table. - Use these calculations to plot additional points on the graph. - Analyze the pattern formed by these points to understand the trajectory described by the parametric equations.
## Trigonometry Exercise: Understanding Parametric Equations ### Problem Statement Given the parametric equations: - \( x = \cos(2t) \) - \( y = \cos(t) \) Fill in the table with the values of \( t \), \( x \), and \( y \), and plot the corresponding points on the graph. ### Table of Values | \( t \) | \( x = \cos(2t) \) | \( y = \cos(t) \) | \( (x, y) \) | |------------|--------------------|-------------------|---------------| | 0 | 1 | 1 | (1, 1) | | \( \pi/4 \)| 0 | \( \approx 0.7 \) | (0, 0.7) | | \( \pi/2 \)| | | | | \( 3\pi/4 \)| | | | | \( \pi \) | | | | | \( 5\pi/4 \)| | | | | \( 3\pi/2 \)| | | | | \( 7\pi/4 \)| | | | | \( 2\pi \) | | | | ### Graph Description The graph is a coordinate plane with axes labeled \( x \) and \( y \) ranging from -8 to 8. A single plotted point, corresponding to \( t = 0 \), \( (x, y) = (1, 1) \), is marked. The graph allows for plotting additional points derived from the completed table to visualize the relationship between \( x \) and \( y \) as \( t \) varies. **Instructions:** - Continue by calculating the other values for \( t \) and complete the table. - Use these calculations to plot additional points on the graph. - Analyze the pattern formed by these points to understand the trajectory described by the parametric equations.
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°.
Related questions
Question
finish the chart and graph please
Transcribed Image Text:## Trigonometry Exercise: Understanding Parametric Equations
### Problem Statement
Given the parametric equations:
- \( x = \cos(2t) \)
- \( y = \cos(t) \)
Fill in the table with the values of \( t \), \( x \), and \( y \), and plot the corresponding points on the graph.
### Table of Values
| \( t \) | \( x = \cos(2t) \) | \( y = \cos(t) \) | \( (x, y) \) |
|------------|--------------------|-------------------|---------------|
| 0 | 1 | 1 | (1, 1) |
| \( \pi/4 \)| 0 | \( \approx 0.7 \) | (0, 0.7) |
| \( \pi/2 \)| | | |
| \( 3\pi/4 \)| | | |
| \( \pi \) | | | |
| \( 5\pi/4 \)| | | |
| \( 3\pi/2 \)| | | |
| \( 7\pi/4 \)| | | |
| \( 2\pi \) | | | |
### Graph Description
The graph is a coordinate plane with axes labeled \( x \) and \( y \) ranging from -8 to 8. A single plotted point, corresponding to \( t = 0 \), \( (x, y) = (1, 1) \), is marked. The graph allows for plotting additional points derived from the completed table to visualize the relationship between \( x \) and \( y \) as \( t \) varies.
**Instructions:**
- Continue by calculating the other values for \( t \) and complete the table.
- Use these calculations to plot additional points on the graph.
- Analyze the pattern formed by these points to understand the trajectory described by the parametric equations.
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