Download 10.7 Polar Coordinates

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
r, 
r
Pole

Polar Axis
Polar Coordinates Into
Rectangular Coordinates
Using Trigonometry
y  r  Sin
x  r  Cos
Finding Using
r  Cos , r  Sin 
r
Pole

Polar Axis
Rectangular Coordinates Into
Polar Coordinates
Using Trigonometry
y
Tan 
x
1  y 
Tan    
x
r x y
2
2
r, 
r
Pole
Polar Axis
2

x
y
Polar Graphpaper
Different ways of writing this same
point in Polar Coordinates
Adding or Subtracting multiplies of 360°
5,30
or
5,390 
or
5,330 
r, 
Different ways of writing this same
point in Polar Coordinates
Or using a negative length and multiplies of
180°
5,30
or
 5,210
or
 5,150
r, 
Polar-to-Rectangular Conversion
Given
 
 4, 
 6
  
 
  
 4,    4  Cos ,4  Sin  
 6 
6
 6 
3
 
Cos  
6 2
  1
Sin  
6 2


3
1
4
,4    2 3 ,2

2
2


Rectangular-to-Polar Conversion
Given
 5,12

12
Tan 
5
1  12 
Tan 
  67.4
 5
 67.4  180  112.6
r   5  12 
2
2
r  25  144
2
r  169  13
13,112.6
2
Changing a Polar equation into a
Rectangular equation
• Given the Polar equation
6
2  3Sin

6
 y 
r
 r  2  3    6

 y 
 r 

 2  3  
 r 

r
6
r
2  3Sin 
Changing a Polar equation into a
Rectangular equation
• Given the Polar equation
6
2  3Sin

6
 y 
r
 r  2  3    6

 y 
 r 

 2  3  
 r 

r
2r  3 y  6
 2r   3 y  6
2
2
4r 2  9 y 2  36 y  36
Changing a Polar equation into a
Rectangular equation
• Given the Polar equation
6
2  3Sin

6
 y 
r
 r  2  3    6

 y 
 r 

2

3

 
 r 

r
2r  3 y  6  2r   3 y  6
2
4r 2  9 y 2  36 y  36
2


4 x 2  y 2  9 y 2  36 y  36
4 x 2  4 y 2  9 y 2  36 y  36
4 x 2  5 y 2  36 y  36  0
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