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μ4c9:T}ElUsing Sketchpad in Calculus -1. Doris Schattschneider
Parametric equations of curves is a main topic in calculus (usually the second semester). Many of the curves for which parametric equations are sought are generated as loci of moving points that are constructed geometrically. The cycloid is a well-known example treated in most calculus texts. Our text, Stewart's "Calculus," treats this in section 9.1. At the end of that section are several problems in which a sketch of a geometrically constructed point is given and the student is asked to find the parametric equations of the locus of the point, and also identify the locus.
The sketch for problem 35 is given above. The question "What is the locus of P, as the ray OQ swings through a full revolution"? is easily answered by dragging Q around the circle in the dynamic sketch (or you can animate Q on the large circle). You can also change the size of each of the circles by dragging Q or S on the radii that are shown in the upper left of the sketch.The student must still find the parametric equations for the locus of P as the ray OQ sweeps around the circle, where the parameter is the angle with initial side the positive x-axis, and terminal side OQ.
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