SAT II Math Level 2 Subject Test Notes: Polar Coordinates

Polar Coordinates In the figure, the rectangular coordinates of  P are  P are ( x,  x, y)  y) and the  polar coordinates of  P are  P are (r  (r ,θ ) P  (x,y )

Polar Coordinates Written as (r  (r ,θ) ,θ) r is r is the distance between a point and the t he origin o θ is the angle between the segment segment and the o  positive x  positive x-axis -axis 

Relationship Between Rectangular and Polar Coordinates: 1.  x = r  r cos cos θ  2.  y = r  r sin sin θ  2 2 2 3.  x + y = r  , using the Pythagorean theorem 

Each point in a plane p lane can be named by an infinite infinite number nu mber of polar coordinates