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Explain why a circle tangent to y=sin(x) at x=π/2 has its center on the vertical line x=π/2. Find the equation of the osculating circle at x=π/2. That is, the circle that is tangent to y=sin(x) and x=π/2 and has the same radius of curvature there.

Explain why a circle tangent to y=sin(x) at x=π/2 has its center on the vertical line x=π/2. Find the equation of the osculating circle at x=π/2. That is, the circle that is tangent to y=sin(x) and x=π/2 and has the same radius of curvature there.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.4: Analytic Proofs
Problem 31E: Suppose that the circle with center 0, 0 and radius length r contains the point a,b. Find the slope...
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Explain why a circle tangent to y=sin(x) at x=π/2 has its center on the vertical line x=π/2. Find the equation of the osculating circle at x=π/2. That is, the circle that is tangent to y=sin(x) and x=π/2 and has the same radius of curvature there.

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