1 Lecture 4 Coordinate Systems: Rectangular, Cylindrical, Spherical.
Spherical Coordinate System
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Transcript of Spherical Coordinate System
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Calculus-III (Section 13.7)
Spherical Spherical Coordinate SystemCoordinate System
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Conversion from Spherical to Conversion from Spherical to Cylindrical Coordinate SystemCylindrical Coordinate System
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RecallRecall
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Cylindrical to Cartesian Spherical to Cylindrical
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Spherical to CartesianSpherical to Cartesian
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Also note that since we know that we get,
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Example -1Example -1Convert the point from Cartesian to Spherical coordinates.
( , , ) (1,1,1)x y z
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1,1,1
1,1,0
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1,1,1
1,1,0
1
4
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2 2 2 2 2 21 1 1 3x y z
1
1cos3
1cos3
z
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Therefore, (1,1,1) in cartesian coordinate system corresponds
1to 3, ,cos in spherical coordinate system.4 3
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Example -2Example -2Convert the point from Cartesian to Spherical coordinates.
( , , ) 1,1, 2x y z
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The first thing that we’ll do here is find .
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Now we’ll need to find
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Finally, we will find Finally, we will find
You find it
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Since the points with coordinates x = -1 and y = 1 lies in the second quadrant,
3 .4
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The spherical coordinates of the
point are then .
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2 2 2 2
2 2
x y z a
aa
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2 2
2 2 2 2 2 2
2 2
cos sin cos sin sin
cos sin cos sincos sin
tan 134
z x y
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Identify the surface 3
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Identify the surface
This is a vertical plane that makes an angle of with the positive x-axis.
3
3
3
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d sinrd d
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