1. Warm Up

2. Converting points and equations
Polar ↔ Rectangular

3. Plotting without graph paper…

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

5. “Equivalent” Points…
Which of the following polar coordinate pairs represent the same point as the point with polar coordinates (2, 105º)?
(-2, -75º)
(-2, 105º)
(-2, -255º)
(2, -75º)
(2, 285º)

6. Point conversion…
Convert the point with polar coordinates to rectangular coordinates…
x = rcos 
y = rsin 

7. (then put  in the correct quadrant)
Point conversion…
Convert the point with rectangular coordinates to polar coordinates…
r2 = x2 + y2
tan  = y/x
(then put  in the correct quadrant)

8. Practice… Convert (-3, -3) to polar coordinates.
NO Calculator…
Convert (-3, -3) to polar coordinates.
Convert (6, π) to rectangular coordinates.
Convert (-4, 2π/3) to rectangular.
Calculator Active… (round to 3 decimal places)
Convert (-2, 5) to polar coordinates. (Degree mode)
Convert (10, 172º) to rectangular coordinates.

9. Equation Conversion Polar to Rectangular
*It’s all about substitution*
Examples:
r = 3
 = /4
r = csc 
r = 2cos 

10. Equation Conversion Rectangular to Polar
*It’s all about substitution*
Examples
x = 2
x2 + y2 = 25
2x + 3y = -3
x2 + y2 - 8x = 0
(x – 4)2 + y2 = 16

11. Practice
Convert the equations from polar to rectangular. Convert the equations from rectangular to polar. 4) x2 – 3y = 0 5) 5x - y = 1 6) (x + 1)2 + (y – 2)2 = 5