MATH-M 311 Lecture Notes - Lecture 1: Ellipse, Hypocycloid, Unit Circle
Document Summary
Section 10. 1 notes- curves defined by parametric equations. 8-26-15 and are functions of additional parameter: often written. Graph of such a curve obtained by plotting for all all real #s. Ex: when , point = (0, 0, (1, 1, 1: (-1, 1, eventually get curve. Graph of has parametric representation: ex. is same as expresses same curve. If centered around another point (a, b), add number to equations: Equation of an ellipse square with the axes (centered, not rotated): o: parametric: A curve does not have a unique set of parametric equations (ex. and : ex. represents unit circle same way as. Moves twice as fast around curve as increases, but traces same pattern. To get angle relative to big circle, divide arc length (relative to both circles) by big radius: as small circle rotates, its center traces circle of radius and goes through angle. Temporarily assume the center of the little circle is at :