This document provides an overview of polar coordinates. It defines polar coordinates as using distance from a fixed point called the pole and an angle from a fixed ray. Points are identified by an ordered pair (r,θ) where r is the distance from the pole and θ is the angle from the horizontal ray. There are multiple representations of a point as (r, θ + 2kπ) or (r, θ + (2k+1)π) for any integer k. Polar equations are written in the form r=f(θ). The distance formula for points in the polar plane is √(r1^2 + r2^2 - 2r1r2cos(θ1-θ2)).

1. Precalculus
9-1 Polar Coordinates
The __________________ coordinate system uses the distance from a fixed point (like
the ___________________) and the angle from a fixed _______________.
• The origin is called the __________________.
• The ______________________________ is the horizontal ray from the pole to
the right.
• A point P is identified by the
coordinates ______________.
• r is the ______________________
from the pole to the point.
• θ is the ________________ from
the
Graph the angle first, then find the distance
along that line.
 7π 
Example 1: Graph P(3, 60°), Q  −1.5,  , and R(-2, -135°).
 8 
There are _____________________ representations of (r, θ):
(r, θ + )
( , θ + (2k + 1)π) where k is any integer.
Polar Equations
A polar equation is in the form:
__________________________________________________________________

2. Basic graphs:
Example 2: Graph (a) r = 3 and
3p
(b) θ =
4
Distance Formula for the polar plane
If P1(r1, θ1) and P2(r2, θ2) are two points in the polar plane, then
P1P2 =
Example 3: While mapping out a level site, a land surveyor identifies a landmark that
is 700 feet away and 40° to the left, and another one 350 feet away and 35° to the right.
What is the distance between the landmarks?
HW p. 558 (16 – 26, 32 – 44 even)