10.6 Polar Coordinates

Hey everyone, so today we learned a new way to graph with the polar coordinate system.


We are all very familiar with the Cartesian Plane or the rectangular coordinate system.

Points are labeled (x,y)
Each set of points represent the directed distances from the coordinate axes to the points.  Each set of points is unique.














Now we are learning about a new coordinate system.
The polar coordinate system consists of concentric circles.  The polar axis is similar to the x axis.

Each point P can be assigned polar coordinates (r,θ)
r represents the distance from the origin (it can be negative)
θ represents the rotation from the polar axis (also can be negative)

Unlike the rectangular coordinate system, points on the polar plane are not unique. The same point can be represented by infinite sets of polar coordinates.  









Now that we know about the polar coordinate system, we can now relate both of the graphs.  Points can be converted from (x,y) to (r,θ) and vice versa.  

Coordinate conversions 

x=rcosθ

y=rsinθ

tanθ=(y/x)

r^2=x^2+y^2

Thats about it!!!

 Helpful video

-Jen Kendall