(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 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
Additional Math Textbook Solutions
Calculus: Early Transcendentals (2nd Edition)
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Intro Stats, Books a la Carte Edition (5th Edition)
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Algebra and Trigonometry (6th Edition)
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