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11.7 Day 2 Spherical coordinatesFor an animation of this topic visit:
http://www.math.umn.edu/~nykamp/m2374/readings/sphcoord/
A Calculator to graph spherical coordinates:http://cs.jsu.edu/mcis/faculty/leathrum/Mathlets/awl/spherical-main.html
For an animation of spherical coordinates visit:
http://www.math.umn.edu/~nykamp/m2374/readings/sphcoord/
Conversions between Spherical and other Coordinate systems
Please record these in your notes
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You do not need to memorize the following formulas but will need to be able to apply them
Spherical coordinates
Cosφ = z/ρρ Cosφ = z
sin φ =r/ ρ
r = ρ sin φ (save this result)
Cosθ = x/r
Cosθ = x/(ρ sin φ )
X= ρ sin φ Cosθ
tanθ = y/x
tanθ = y/( ρ sin φ Cosθ) (from previous slide)
tanθ (ρ sin φ Cosθ) = y
sin θ (ρ sin φ Cosθ) =yCosθ
y = ρ sin φ sin θ
Example 5a
Find an equation in spherical coordinates for the surface represented by the rectangular equation.
Example 5 b
Find an equation in spherical coordinates for the surface represented by the rectangular equation.
Changing between coordinates on the TI 89
Press 2nd 5 (math) – 4 matrices – L Vecor opsto sphereTo convert rectangular to Polar (2 D)[1,2,3] to sphere (to is expressed with a triangle)
Note: You can change from rectangular to polar, cylindrical or spherical
Or change from polar to rectangular with built in functions
One use of spherical coordinates:
Image: Bosch 36W column loudspeaker polar pattern
For more information visit:http://en.wikipedia.org/wiki/Polar_coordinates