A pair of parametric equations is given. x = 9t², y = 27t³ (a) Sketch the curve represented by the parametric equations. Use arrows to indicate the direction of the curve as t increases. y y -10 -5 10 -5 -10 5 لل 10 -10 -5 10 -10 5 10 X
A pair of parametric equations is given. x = 9t², y = 27t³ (a) Sketch the curve represented by the parametric equations. Use arrows to indicate the direction of the curve as t increases. y y -10 -5 10 -5 -10 5 لل 10 -10 -5 10 -10 5 10 X
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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Transcribed Image Text:The image presents a mathematical graph along with a question for students to solve.
**Graph Explanation:**
- The graph is a Cartesian plane displaying two red curves, which are asymptotic in nature.
- The curves appear to form sections of a hyperbola opening sideways, with arrows indicating the direction from the left curve up towards the right and the right curve down towards the left.
- The x-axis ranges from -10 to 10 and the y-axis ranges from -10 to 10.
**Question:**
(b) Find a rectangular-coordinate equation for the curve by eliminating the parameter.
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- Buttons labeled "Read It" and "Watch It" are available for students seeking more help.
![**Parametric Equations and Their Graphs**
A pair of parametric equations is given:
\[ x = 9t^2, \quad y = 27t^3 \]
**Task (a):** Sketch the curve represented by the parametric equations. Use arrows to indicate the direction of the curve as \( t \) increases.
**Graph Descriptions:**
1. **Top-Left Graph:**
- The graph displays a curve originating from the origin (0,0) and moving downward in the third quadrant. It then curves up through the origin and moves upward into the first quadrant.
- Arrows are present on the curve, indicating the direction of increasing \( t \) from the third quadrant, passing through the origin, and continuing into the first quadrant.
2. **Top-Right Graph:**
- The graph displays a curve similar to an upside-down parabola centered at the x-axis. It begins in the second quadrant and decreases to the x-axis before moving into the fourth quadrant.
- Arrows on the graph show the direction of increasing \( t \) from left to right, starting in the second quadrant, passing through the origin, and extending into the fourth quadrant.
3. **Bottom-Left Graph:**
- This graph presents an upward curve beginning from the origin and moving toward the first quadrant.
- An arrow indicates the direction of increasing \( t \), starting from the origin and moving upwards into the first quadrant.
4. **Bottom-Right Graph:**
- The graph resembles an upright parabola along the x-axis, originating in the third quadrant and ascending towards the x-axis and into the second quadrant.
- Arrows indicate the direction of \( t \), progressing from the third quadrant, moving towards the origin, and extending into the second quadrant.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61d8af2b-7fdf-4a8e-a1bf-75f5ea698050%2F8fa5afbd-5e63-4cd5-9c8f-694ddef60dfb%2Fbkug1is_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Parametric Equations and Their Graphs**
A pair of parametric equations is given:
\[ x = 9t^2, \quad y = 27t^3 \]
**Task (a):** Sketch the curve represented by the parametric equations. Use arrows to indicate the direction of the curve as \( t \) increases.
**Graph Descriptions:**
1. **Top-Left Graph:**
- The graph displays a curve originating from the origin (0,0) and moving downward in the third quadrant. It then curves up through the origin and moves upward into the first quadrant.
- Arrows are present on the curve, indicating the direction of increasing \( t \) from the third quadrant, passing through the origin, and continuing into the first quadrant.
2. **Top-Right Graph:**
- The graph displays a curve similar to an upside-down parabola centered at the x-axis. It begins in the second quadrant and decreases to the x-axis before moving into the fourth quadrant.
- Arrows on the graph show the direction of increasing \( t \) from left to right, starting in the second quadrant, passing through the origin, and extending into the fourth quadrant.
3. **Bottom-Left Graph:**
- This graph presents an upward curve beginning from the origin and moving toward the first quadrant.
- An arrow indicates the direction of increasing \( t \), starting from the origin and moving upwards into the first quadrant.
4. **Bottom-Right Graph:**
- The graph resembles an upright parabola along the x-axis, originating in the third quadrant and ascending towards the x-axis and into the second quadrant.
- Arrows indicate the direction of \( t \), progressing from the third quadrant, moving towards the origin, and extending into the second quadrant.
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