Involute Problem: A string is wrapped around a circle with radius 1 in. As the string is

Chapter 4, Problem 11

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Involute Problem: A string is wrapped around a circle with radius 1 in. As the string is unwound, its end traces a path called the involute of a circle (Figure 4-7k). The parametric equations of this involute are x = cos t + t sin t y = sin t t cos t where t is the number of radians from the positive x-axis to the radius drawn to the point of tangency of the string.Figure 4-7ka. Use your grapher to confirm that theseparametric equations give the graph shownin Figure 4-7k.b. Find dy/dx in terms of t. Simplify as muchas possible.c. Show that the value you get for dy/dx att = is consistent with the graph.