Consider the following. x = 3 sin(68), y = 3 cos(68), Oses" (a) Eliminate the parameter to find a Cartesian equation of the curve. (b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. -3 3 G
Consider the following. x = 3 sin(68), y = 3 cos(68), Oses" (a) Eliminate the parameter to find a Cartesian equation of the curve. (b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. -3 3 G
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![## Consider the following:
\( x = 3 \sin(6\theta) \), \( y = 3 \cos(6\theta) \), \( 0 \leq \theta \leq \frac{\pi}{3} \)
### (a) Problem Statement
Eliminate the parameter to find a Cartesian equation of the curve.
\[ \text{[Text box for answer]} \]
### (b) Graphical Representation
**Instructions:** Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases.
#### Graph Descriptions:
1. **Graph (O):**
- Appears to show a circle centered at the origin with a radius of 3.
- The direction arrow indicates the curve is traced counterclockwise.
2. **Graph (P):**
- Depicts a semicircle in the upper half of the coordinate plane, starting from \(x = 3\) to \(x = -3\).
- The arrow indicates the curve is traced from right to left.
3. **Graph (Q):**
- Shows a semicircle in the lower half of the coordinate plane, starting from \(x = -3\) to \(x = 3\).
- The arrow indicates the curve is traced from left to right.
Each graph represents a section or transformation of the original parametric curve based on the specified range of \(\theta\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd29508f4-fc1e-4105-bc30-f2f3b3e53ddd%2F4e1df8aa-bc7a-409e-8df3-c8dfb0d805b8%2Fwcmyjii_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Consider the following:
\( x = 3 \sin(6\theta) \), \( y = 3 \cos(6\theta) \), \( 0 \leq \theta \leq \frac{\pi}{3} \)
### (a) Problem Statement
Eliminate the parameter to find a Cartesian equation of the curve.
\[ \text{[Text box for answer]} \]
### (b) Graphical Representation
**Instructions:** Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases.
#### Graph Descriptions:
1. **Graph (O):**
- Appears to show a circle centered at the origin with a radius of 3.
- The direction arrow indicates the curve is traced counterclockwise.
2. **Graph (P):**
- Depicts a semicircle in the upper half of the coordinate plane, starting from \(x = 3\) to \(x = -3\).
- The arrow indicates the curve is traced from right to left.
3. **Graph (Q):**
- Shows a semicircle in the lower half of the coordinate plane, starting from \(x = -3\) to \(x = 3\).
- The arrow indicates the curve is traced from left to right.
Each graph represents a section or transformation of the original parametric curve based on the specified range of \(\theta\).
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