10.6: Polar Coordinates Introduction

Today we learned about a new way to graph. Instead of having (x, y), we now have (r, Ɵ). 

The graph of polar coordinates will look something like this: 

The r counts out from the center and the Ɵ on the corresponding labeled lines. Polar coordinates can also be negative. If a r or Ɵ is negative, then then move opposite. For instance, if the point is (1, pi/12), then the point would be on the first circle from the center and in quadrant 2 (top right), but if the point is (-1, -pi/12) then the point would be on the first circle in the center in quadrant 4 (bottom left) and on the line labeled 13pi/12. 

Sometimes you will have to convert between polar equations and rectangular equations. To do this, use these equations. 

When converting from polar to rectangular, use these equations: 
x=rcosƟ
y=rsinƟ

When converting from rectangular to polar, use these equations. 
tanƟ=y/x
r^2=x^2=y^2

If you need more help, check out Miss V's lecture: 
https://docs.google.com/file/d/0B0qanadSJ9JgWlpnSEdVRGZya3c/edit

Math joke of the day:
A quote from Charles Darwin: "A mathematician is a blind man in a dark room looking for a black cat which isn't there."