(BQ) Part 2 book "Calculus early transcendentals" has contents: Parametric equations and polar coordinates, infinite sequences and series, vectors and the geometry of space, vector functions, partial derivatives, vector calculus, second order differential equations. | 9/22/10 9:54 AM Page 635 10 Parametric Equations and Polar Coordinates The Hale-Bopp comet, with its blue ion tail and white dust tail, appeared in the sky in March 1997. In Section you will see how polar coordinates provide a convenient equation for the path of this comet. © Dean Ketelsen So far we have described plane curves by giving y as a function of x ͓y f ͑x͔͒ or x as a function of y ͓x t͑y͔͒ or by giving a relation between x and y that defines y implicitly as a function of x ͓ f ͑x, y͒ 0͔. In this chapter we discuss two new methods for describing curves. Some curves, such as the cycloid, are best handled when both x and y are given in terms of a third variable t called a parameter ͓x f ͑t͒, y t͑t͔͒. Other curves, such as the cardioid, have their most convenient description when we use a new coordinate system, called the polar coordinate system. 635 Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 9/22/10 9:54 AM Page 636 636 CHAPTER 10 PARAMETRIC EQUATIONS AND POLAR COORDINATES Curves Defined by Parametric Equations y C (x, y)={ f(t), g(t)} 0 x Imagine that a particle moves along the curve C shown in Figure 1. It is impossible to describe C by an equation of the form y f ͑x͒ because C fails the Vertical Line Test. But the x- and y-coordinates of the particle are functions of time and so we can write x f ͑t͒ and y t͑t͒. Such a pair of equations is often a convenient way of describing a curve and gives rise to the .
