Polar Graphs Day 1

What we did in class is learn how to graph polar equations. There are a few identities that are helpful to use for graphing the equations, they are: cos(-x)=cos(x) sin(-x)=-sin(x) sin(a-b)=sin(a)cos(b)-sin(b)cos(a) cos(a-b)=cos(a)cos(b)+sin(a)sin(b)

Before graphing you must test for symmetry. To test for x-axis symmetry (polar axis) you plug in (r,-x) to test for y-axis symmetry ( axis) you plug in (r, pi-x ) and to test origin symmetry (pole) you plug in (-r,x) and for all of these if you get the same equation you started with there is symmetry if you don't then you MIGHT have symmetry

Examples:

r=2-2sin(x)

Tests

polar axis:

r=2-2sin(-x)

r=2+2sin(x) (maybe)

y-axis:

(yes)

Origin:

-r=2-2sin(x) (maybe)

Example 2:

Polar axis:

(yes)

y-axis:

(Maybe)

Origin:

-r=2-cos(x)

Maybe















If you need more help go to mr. corn's website and the notes are on here.