To Prove: The parametric equations of the trochoid are
Answer to Problem 38E
The parametric equations are
Explanation of Solution
Given:
The given equations are
The given condition are
Calculation:
Consider the case for
Consider the point
The required diagram is shown in Figure 1
Figure 1
The distance between the centre of the circle and origin is
Here, the distances are,
Consider the coordinates of
Also,
Thus, the parametric equations are,
Consider the case for
The required sketch for
Figure 2
The sketch for
Figure 3
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