Polar Coordinates 11.3

What is a coordinate system? Where’s Granny’s house? A coordinate system assigns a numerical representation of position of a point space (or the plane). Common systems: –Cartesian ‘x-y’ grid –Polar –Cylindrical –Spherical Polar

Cartesian  Polar Coordinates Polar from Cartesian Cartesian from Polar

So – why do we need this? Sometimes the symmetry of the situation makes one coordinate system more “natural” Sometimes mathematical operations and expressions are simpler in one coordinate system than another Sometimes unexpected insights emerge when you change coordinate systems Having a variety of coordinates systems enlarges your “math vocabulary” and allows you to express ideas more clearly

Polar Plots Are not tales of the far north! Are graphs relating r and  –Example:

Try some… What do the following look like? –A) –B) –C)

Tangents to Polar Curves… How can you find the slope on a polar plot? Answer – start with and use the conversion from cartesians to polars Try this on the previous 3 examples

Other examples… –25,37,45,54,63 Try to graph these using the graphing applet (or in Maple): –

Areas in Polar Form Let’s investigate the following…