Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.1 Parametric Equations - Exercises - Page 603: 42


The answer is $c(t)=(2\cos(t+\frac{\pi}{3}),2\sin(t+\frac{\pi}{3})$.

Work Step by Step

This is the equation of the circle of radius 2 centered at the origin. The parametrization is given by $c(t)=(2\cos t,2\sin t)$. At $t=0$, we have $(x(0),y(0))=(1,\sqrt{3})$. So, we may take $x(t)=2\cos(t+\frac{\pi}{3})$. So, $y(t)=2\sin(t+\frac{\pi}{3})$. Thus, the parametrization of $x^2+y^2=4$ is $c(t)=(2\cos(t+\frac{\pi}{3}),2\sin(t+\frac{\pi}{3})$ for $0\leq t\leq 2 \pi$.
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