Polar Coordinates
Definitions
Polar Coordinate System
(
Cartesian Coordinate System
y
)
(
Converting between Cartesian and Polar
)
y
(
r
x
)
r
y
(Pythagorean)
x
x
x
Polar to Cartesian
Cartesian to Polar
Conversion
Conversion
Tangents to Polar Curves
Found using
and
Problems
I.
Write the Cartesian equations from the given Polar equations
a)
b)
c)
( )
tan(
(
(
II.
)
)
)
Write the Polar equations from the given Cartesian equations
a)
c)
b)
(
(
)
)
(
)
(
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)
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Problems (continued)
III.
Sketch the Curve by first converting to Cartesian
a)
(
)
(Cardioid)
(
)
0
2
1
0
0
2
-1
4
0
2
b)
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c)
(
)
0
0
1
0
-1
0
1
0
-1
0
c)
(
)
(
0
)
1
0
-1
0
1
0
-1
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Problems (continued)
IV.
Find the slope of the tangent line to the following polar curve
(
)
Given:
(
)
(
(
)
(
)
)
√
Alternate Approach:
(
)
Then:
(
)
(
)
(
)
(
(
)
)
(
)
√
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