1 Parametric curves Consider the parametric function r(t) = sin(t) y(t) = 2-sin(t) (1) Show that this traces a line segment in the (x, y) plane. What are the end-points of that segment? (Provide the z and y coordinates of both points). Coordinates of the first end point. Coordinates of the second end point (2) As the point (r(t), y(t)) travels on the segment, what is its distance to the origin. Call this the function D(t)? The distance to the origin is the function D(t) = (3) Using Calculus, find the time at which the point is closest to the origin, and show that it hap- pens on one of the end points.

1 Parametric curves Consider the parametric function r(t) = sin(t) y(t) = 2-sin(t) (1) Show that this traces a line segment in the (x, y) plane. What are the end-points of that segment? (Provide the z and y coordinates of both points). Coordinates of the first end point. Coordinates of the second end point (2) As the point (r(t), y(t)) travels on the segment, what is its distance to the origin. Call this the function D(t)? The distance to the origin is the function D(t) = (3) Using Calculus, find the time at which the point is closest to the origin, and show that it hap- pens on one of the end points.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter8: Polar Coordinates And Parametric Equations

Section8.CR: Chapter Review

Problem 43E

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