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For an animation of spherical coordinates visit:

11.7 Day 2 Spherical coordinates For 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:

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For an animation of spherical coordinates visit:

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  1. 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

  2. For an animation of spherical coordinates visit: http://www.math.umn.edu/~nykamp/m2374/readings/sphcoord/

  3. The Spherical Coordinate System

  4. Conversions between Spherical and other Coordinate systemsPlease record these in your notes __ You do not need to memorize the following formulas but will need to be able to apply them

  5. Spherical coordinates r (due to opposite sides of a parallelogram)

  6. Spherical coordinates Cosφ = z/ρ ρ 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

  7. tanθ = y/x tanθ = y/( ρ sin φ Cosθ) (from previous slide) tanθ (ρ sin φ Cosθ) = y sin θ (ρ sin φ Cosθ) =y Cosθ y = ρ sin φ sin θ

  8. Converting between coordinate systems

  9. Example 5a Find an equation in spherical coordinates for the surface represented by the rectangular equation.

  10. Solution to example 5a Cone: x2 + y 2 = z2

  11. Example 5 b Find an equation in spherical coordinates for the surface represented by the rectangular equation.

  12. Solution to 5b

  13. Common equations in spherical coordinates

  14. Converting between coordinate systems

  15. Do examples from text book P. 825 # 58,76, cylindrical 76 (76 is shown on the next slide_

  16. Changing between coordinates on the TI 89 Press 2nd 5 (math) – 4 matrices – L Vecor ops to sphere To 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

  17. One use of spherical coordinates:Image: Bosch 36W column loudspeaker polar patternFor more information visit:http://en.wikipedia.org/wiki/Polar_coordinates

  18. A math sing along • ρρρ … Row, Row, Row your boat … By Mr. Whitehead

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