Pre-Calculus Notes Name: ______________________ Section 10.7 - Polar Coordinates Example 2: Find three additional polar representations for each of the following points. a. ( )5,40P with 360 360θ− < < b. 7,

3P π −

with 2 2π θ π− < <

Example 3: Graph each polar equation on the Cartesian plane. a. 4r = b. 2.5θ = −

Recall from last semester:

cosxr

θ= , when solved for x , becomes ________________________________.

sinyr

θ= , when solved for y , becomes ________________________________.

tanyx

θ= , when solved for θ , becomes ________________________________.

And don’t forget that 2 2x y+ = ______________.

Cartesian Coordinates: _________ Polar Coordinates: _____________

Example 1: Graph AND label each of the following polar coordinates.

330°

300°

270°

240°

210°

180°

150°

120°

90°

60°

30°

0°

( ) ( )( ) ( )( ) ( )( ) ( )( )

3,45 3, 45

3,45 3, 45

3,225 3,315

3,225 3,0

0,135

A B

C D

E F

G H

I

−

− − −

−

y

x

y

x

( ),x y are called rectangular coordinates. ( ),r θ are called polar coordinates.

Converting Polar to Rectangular Converting from Rectangular to Polar cosx r θ= and siny r θ= 1 yTan

xθ − =

(but double check your quadrant!) and 2 2 2x y r+ =

Example 4: Convert each POLAR point ( ),r θ to a RECTANGULAR point ( ),x y . SHOW YOUR WORK.

a. ( )2,π b. 3,

6π

c. ( )1.3,2.35−

Use a calculator.

Example 5: Convert each RECTANGULAR point ( ),x y to a POLAR point ( ),r θ . SHOW YOUR WORK.

a. ( )1,1−

b. ( )0,2 c. ( )2, 1−

Use a calculator.

Example 6: Convert the rectangular equations to polar form. a. 2 2 49x y+ =

b. 2y x=

Example 7: Convert the polar equations to rectangular form. a. 2 2r = b. 4cos rθ =

c. 3πθ =

d. secr θ=