Worksheet 4 Math 126
The goal of this worksheet is to get familiar with the use of polar coordinates
and to practice the conversion from polar coordinates to Cartesian and vice
versa.
You should observe that some regions are easier to understand in
Cartesian coordinates whereas for others the choice of polar coordinates is
much more suitable.
The skill of being able to chose the right coordinate
system will be invaluable when we start evaluating double integrals as in
chapter 15. Later on you may wish to compare the regions you sketch today
with the ones in problems 16, Section 15.4.
The following trig identity will be useful for the worksheet:
sin(
α
+
β
) = sin(
α
) cos(
β
) + cos(
α
) sin(
β
)
cos(
α
+
β
) = cos(
α
) cos(
β
)

sin(
α
) sin(
β
)
And here are the conversion formulas
x
=
r
cos
θ,
y
=
r
sin
θ
r
2
=
x
2
+
y
2
,
tan
θ
=
y
x
1. Describe each curve (region) below in Cartesian coordinates.
Then
sketch the curve (region). Indicate which coordinate system you used
for sketching.
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 Spring '07
 Smith
 Cartesian Coordinate System, Polar Coordinates, Coordinate system, Spherical coordinate system, Polar coordinate system, Coordinate systems

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