(a)
To find: The parametric equation for the involute by expressing the coordinates
(a)
Answer to Problem 51E
The required parametric equation is
Explanation of Solution
Given Data:
The given diagram is shown in Figure 1
Figure 1
Calculation:
Consider the initial point of the tracing is
Then, from the above data and the geometry of the figure shows that the parametric equation of the involute is,
(b)
To find: The length of the involute for
(b)
Answer to Problem 51E
The required length is
Explanation of Solution
Consider the parametric equation are,
The derivative with respect to t is,
Then, the derivative of
Consider the length of the parametric curve is obtained as,
Then, for the interval
Solve further as,
Chapter 11 Solutions
Calculus: Graphical, Numerical, Algebraic
Additional Math Textbook Solutions
Calculus & Its Applications (14th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
University Calculus: Early Transcendentals (3rd 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