1. Chapter 10 Parametric Equations and Polar Coordinates

2. 10.1 Polar coordinates
The point o is called the pole
The point P is represented by the
ordered pair (r, θ) and r,θ are call-
ed polar coordinates of P
θis positive if measure in the cou-
nterclockwise direction from the po-
lar axis and negative in the clockwi-
se direction
Polar axis
P(r, θ) r θ
(r, θ)
(-r, θ) θ
The points (r, θ) and (-r, θ) lie
on the same line through o and at
the same distance |r | from o

3. Example Plot the points whose polar coordinates are given
Solution

5. The connection between polar and Cartesian
coordinates y r θ
P(x,y)=p(r,θ)

6. Example Identify the curve by finding a Cartesian equation
for the curve
Solution

7. Example Find a polar equation for the curve represented
by the given cartesian equation
Solution