11.7 Day 2 Spherical coordinates For an animation of this topic visit: A Calculator to graph spherical coordinates:

For an animation of spherical coordinates visit: u/~nykamp/m2374/re adings/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/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

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

Converting between coordinate systems

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

Solution to example 5a Cone: x 2 + y 2 = z 2

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 2 nd 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

One use of spherical coordinates: Image: Bosch 36W column loudspeaker polar pattern For more information visit: wiki/Polar_coordinates

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