Cornu Spiral Consider the cornu spiral given by
(a) Use a graphing utility to graph the spiral over the interval
(b) Show that the cornu spiral is symmetric with respect to the origin.
(c) Find the length of the comu spiral from
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Chapter 10 Solutions
Bundle: Calculus, 10th + WebAssign Printed Access Card for Larson/Edwards' Calculus, 10th Edition, Multi-Term
- A circle C of radius 2r has its center at the origin. A circle of radius r rolls without slipping in the counterclockwise direction around C. A point P is located on a fixed radius of the rolling circle at a distance b from its center, 0<b<r. Let L be the line from the center of C to the center of the rolling circle and t be the angle that L makes with the positive x-axis. Parametric equations of the path traced out by P are x(t) = 3r cos t + b cos 3t and y(t) = 3r sin t + b sin 3t Show that an equilateral triangle can be inscribed in the epitrochoid and that its centroid is on a circle of radius b centered at the center of the epitrochoid.arrow_forwardUse cylindrical coordinates. (a) Find the volume of the solid that the cylinder r = a cos θ cuts out of the sphere of radius a centered at the origin, show how you obtained the range for θ. (b) Illustrate the solid of part (a) by graphing the sphere and the cylinder on the same screen.arrow_forwardUse a graphing utility to graph each set of parametric equations. x = t − sin t, y = 1 − cos t, 0 ≤ t ≤ 2π x = 2t − sin(2t), y = 1 − cos(2t), 0 ≤ t ≤ π (a) Compare the graphs of the two sets of parametric equations in earlier part. When the curve represents the motion of a particle and t is time, what can you infer about the average speeds of the particle on the paths represented by the two sets of parametric equations?arrow_forward
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