MATH 2004 Parametric Equations and Polar Coordinates Notes...

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Term: Fall 2012Course: MATH 2004Instructor: Minyi Huang1Chapter 10. Parametric Equations and Polar Coordinates1NotesFirst version: 2012-09-131.1Parametric equations
Example 3Find the parametric equations of the circle with radiusrandcenter(h,k).
Term: Fall 2012Course: MATH 2004Instructor: Minyi Huang2-1012345678-1012345Figure 1: The cycloid withr=0.5.Example 4The cycloid:x=r(θ-sinθ)andy=r(1-cosθ),θR.This is the curve traced out by a pointPon the circumference of a circle ofradiusras the circle moves along a straight line.Example 5Sketch the curve forx=sintandy=sin2t. We havey=x2.Question: what is the range ofx?
Example 6Letx=sintandy=cos2t, 0tπ/2. Graph the curve.
Term: Fall 2012Course: MATH 2004Instructor: Minyi Huang3

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