Upload
fineen
View
98
Download
4
Tags:
Embed Size (px)
DESCRIPTION
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: - PowerPoint PPT Presentation
Citation preview
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/
The Spherical Coordinate System
Conversions between Spherical and other Coordinate systems
Please record these in your notes
__
You do not need to memorize the following formulas but will need to be able to apply them
Spherical coordinates
r (due to opposite sides of a parallelogram)
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
Converting between coordinate systems
Example 5a
Find an equation in spherical coordinates for the surface represented by the rectangular equation.
Solution to example 5aCone: x2 + y 2 = z2
Example 5 b
Find an equation in spherical coordinates for the surface represented by the rectangular equation.
Solution to 5b
Common equations in spherical coordinates
Converting between coordinate systems
Do examples from text book
P. 825 # 58,76,
(76 is shown on the next slide_
76
cylindrical
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
A math sing along
• ρρρ …
Row, Row, Row your boat …
By Mr. Whitehead