James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

10
Parametric Equations and
Polar Coordinates
The photo shows Halley’s
comet as it passed Earth in
1986. Due to return in 2061,
it was named after Edmond
Halley (1656–1742), the
English scientist who first
recognized its periodicity. In
Section 10.6 you will see how
polar coordinates provide a
convenient equation for the
elliptical path of its orbit.
Stocktrek / Stockbyte / Getty Images
So far we have described plane curves by giving y as a function of x fy − f sxdg or x as a
function of y fx − tsydg or by giving a relation between x and y that defines y implicitly as a function
of x f f sx, yd − 0g. 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 fx − f std, y − tstdg. Other curves, such as the cardioid, have
their most convenient description when we use a new coordinate system, called the polar coordinate
system.
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