Polar Coordinates
Plotting Polar Points (r , θ)
ex) Plot the following points on the polar grid below
A (r , θ) = (4,315°)
B (r , θ) = (6, 23π )
C (r , θ) = (−5,90°)
D (r , θ) = (7, − 34π )
E (r , θ) = (−7, π4 )
There are an infinite number of ways to represent the same point in polar
coordinates.
ex) Determine an equivalent representation for the point (r , θ) = (6,150°)
a) using r < 0 and 0 ≤ θ ≤ 360°
b) using r > 0 and −360° ≤ θ ≤ 0°
c) using r < 0 and 360° ≤ θ ≤ 720°
Coordinate Conversions between Polar (r , θ) and Rectangular (x , y)
To convert (x , y) into (r , θ)
To convert (r , θ) into (x , y)
ex) Make the following coordinate conversions:
a) Convert (r , θ) = (6,150°) into rectangular coordinates (x , y)
b) Convert (x , y) = (0, −10) into polar coordinates (r , θ)
You can also use these to convert between (x , y) equations and (r , θ) equations
ex) a) Convert the rectangular equation x 2 + y 2 = 25 into polar form.
b) Convert the polar equation r =
5
into rectangular form.
cos θ
4
look like?
cos θ − 2sinθ
What is its rectangular conversion?
ex) What does the graph of r =
ex) What does the graph of θ = π /6 look like?
What is its rectangular conversion?
Graphing Polar Equations
ex) Sketch the graph of r = 8cos θ
(use a table of values on your calculator)
(Use ‘POLAR’ mode)
(can’t graph this one in POLAR mode)
ex) Sketch the graph of r = 3 − 3sinθ
ex) Sketch the graph of r = 2 + 4cos θ
ex) Sketch the graph of r 2 = 9sin(2θ)
POLAR GRAPH PAPER