(a)
To find: The parametric equation for the particle that moves counter clockwise halfway around the circle from the top and bottom.
(a)
Answer to Problem 32RE
The parametric equation is
Explanation of Solution
Given:
The given equation is
Calculation:
The general form for the parametric equation of the circle with the centre at
The range of
Consider the given equation of the circle is,
Then, the parametric equation is,
As the path of the particle is in counter clockwise direction from the top to the bottom, the value of
The parametric equation is
(b)
To find: The graph for the semi-circular path.
(b)
Explanation of Solution
Given:
The given equation is
Calculation:
Consider the parametric equation are,
Consider the parameter range is,
The table for the value of
Table 1
0.5858 | 1.414 | |
0 | 0 | |
0.5858 | -1.414 | |
2 | -2 |
The graph for the parametric equations is shown in Figure 1
Figure 1
Chapter 1 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning