Find parametric equations and a parameter interval for the motion of a particle that starts at the point (−2, 0) in the xy-plane and traces the circle x2+y2=4 three times clokwise.

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Find parametric equations and a parameter interval for the motion of a particle that starts at the point (−2, 0) in the xy-plane and traces the circle x2+y2=4 three times clokwise.

Troy Lesure · Accepted Answer

Step 1&amp;nbsp;Idea employed:Parametric equation:&amp;nbsp;x=r×cos⁡θ&amp;nbsp;and&amp;nbsp;y=r×sin⁡θ&amp;nbsp;Equation of circle is&amp;nbsp;x2+y2=r2&amp;nbsp;There, r is radius&amp;nbsp;Step 2&amp;nbsp;The equation&amp;nbsp;x2+y2=4&amp;nbsp;can be written as,&amp;nbsp;x2+y2=22&amp;nbsp;Compare&amp;nbsp;x2+y2=22&amp;nbsp;with&amp;nbsp;x2+y2=r2&amp;nbsp;to obtain r&amp;nbsp;r=2&amp;nbsp;Consequently, the form of the parametric equations isx=2×cos⁡θ&amp;nbsp;and&amp;nbsp;y=2×sin⁡θ&amp;nbsp;The particle that starts at the point&amp;nbsp;(−2,&amp;nbsp;0), therefore, the parametric equation is&amp;nbsp;x=−2×cos⁡θ&amp;nbsp;and&amp;nbsp;y=2×sin⁡θ&amp;nbsp;The three clockwise rotations signify3(2π)=6π&amp;nbsp;Thus, the parametric equation is&amp;nbsp;x=−2×cos⁡θ&amp;nbsp;and&amp;nbsp;y=2×sin⁡θ, and interval is&amp;nbsp;0≤θ≤6π

Find parametric equations and a parameter interval for the motion

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