10.7 polar coordinates
DESCRIPTION
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. http://wordnetweb.princeton.edu/perl/webwn?s=polar%20coordinate. - PowerPoint PPT PresentationTRANSCRIPT
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