10.7 Polar Coordinates

Polar Axis

Definition of Polar Coordinates

Polar Coordinates are two values that locate a point on a plane by its distance from a fixed pole and its angle from a fixed line passing through the pole

AxisPolar

r

,r

Pole

http://wordnetweb.princeton.edu/perl/webwn?s=polar%20coordinate

Polar Coordinates Into Rectangular Coordinates

Using Trigonometry Finding Using

AxisPolar

r

Pole

Cosrx

Sinry

SinrCosr ,

Rectangular Coordinates Into Polar Coordinates

Using Trigonometry

AxisPolar

r

Pole

222 yxr

,ry

x

x

yTan

x

yTan

1

Polar Graphpaper

Different ways of writing this same point in Polar Coordinates

Adding or Subtracting multiplies of 360°

,r

330,5

390,5

30,5

or

or

Different ways of writing this same point in Polar Coordinates

Or using a negative length and multiplies of 180°

,r

150,5

210,5

30,5

or

or

Polar-to-Rectangular Conversion

Given

2,322

14,

2

34

2

1

6

2

3

6

64,

64

6,4

Sin

Cos

SinCos

6,4

Rectangular-to-Polar Conversion

Given

12,5

13169

14425

1252

222

r

r

r

6.112,13

6.1121804.67

4.675

125

12

1Tan

Tan

Changing a Polar equation into a Rectangular equation

• Given the Polar equation

Sinr

32

6

632

32

6

32

6

r

yr

ry

r

Sinr

Changing a Polar equation into a Rectangular equation

• Given the Polar equation

632

32

6

32

6

r

yr

ry

r

Sinr

363694

632

632

22

22

yyr

yr

yr

Changing a Polar equation into a Rectangular equation

• Given the Polar equation

363694

632632

632

32

6

32

6

22

22

yyr

yryr

r

yr

ry

r

Sinr

0363654

3636944

363694

22

222

222

yyx

yyyx

yyyx

Homework

Page 754 – 755

# 5, 10, 15, 25,

35, 45, 55, 65,

70, 75a

Homework

Page 754 – 755

# 31, 36, 41, 51,

56, 61, 69