Parametric Equations and Polar Coordinates

So far, we’ve sketched the graphs of many equations of the form *y* = *f*(*x*) with respect to Cartesian coordinates. Now we’re going to look at things in a different way: first, we’ll look at what happens when the coordinates *x* and *y* are not directly related, but are instead related by a common parameter; and then we’ll see what happens when we replace the whole darn coordinate system with something entirely different. Of course, we have to do some calculus too. So here’s the program for this chapter:

• parametric equations, graphs and finding tangents;

• converting from polar coordinates to Cartesian coordinates, and vice versa;

• finding tangents to polar curves; ...

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