1. Polar Coordinates
Lesson 10.5

2. Points on a Plane Rectangular coordinate system
Represent a point by two distances from the origin
Horizontal dist, Vertical dist
Also possible to represent different ways
Consider using dist from origin, angle formed with positive x-axis
(x, y) •
(r, θ) • r θ

3. Plot Given Polar Coordinates
Locate the following

4. Find Polar Coordinates
What are the coordinates for the given points?
• A
A =
B =
C =
D =
• B
• D
• C

5. Converting Polar to Rectangular
Given polar coordinates (r, θ)
Change to rectangular
By trigonometry
x = r cos θ y = r sin θ
Try = ( ___, ___ ) • r y θ x

6. Converting Rectangular to Polar•
Given a point (x, y)
Convert to (r, θ)
By Pythagorean theorem r2 = x2 + y2
By trigonometry
Try this one … for (2, 1)
r = ______
θ = ______ r y θ x

7. It is θ (the 2nd element that is the independent variable
Polar Equations
States a relationship between all the points (r, θ) that satisfy the equation
Example r = 4 sin θ
Resulting values
Note: for (r, θ)
It is θ (the 2nd element that is the independent variable
θ in degrees

8. Graphing Polar Equations
Set Mode on TI calculator
Mode, then Graph => Polar
Note difference of Y= screen

9. Graphing Polar Equations
Also best to keep angles in radians
Enter function in Y= screen

10. Graphing Polar Equations
Set Zoom to Standard,
then Square

11. Try These! For r = A cos B θ r = 3 sin 2θ r = 4 cos 3θ
Try to determine what affect A and B have
r = 3 sin 2θ
r = 4 cos 3θ
r = sin 4θ

12. Application Parabolic antenna reflector for wireless router
Note measurements of antenna effectiveness at website

13. Assignment Lesson 10.5A Page 433 Exercises 1 – 45 odd Lesson 10.5B