Unit 11.7: Cylindrical and Spherical Coordinates

0.0(0)
Studied by 0 people
call kaiCall Kai
learnLearn
examPractice Test
spaced repetitionSpaced Repetition
heart puzzleMatch
flashcardsFlashcards
GameKnowt Play
Card Sorting

1/20

encourage image

There's no tags or description

Looks like no tags are added yet.

Last updated 10:07 PM on 6/4/26
Name
Mastery
Learn
Test
Matching
Spaced
Call with Kai

No analytics yet

Send a link to your students to track their progress

21 Terms

1
New cards
Cylindrical to rectangular
x=rcosθ
2
New cards
Cylindrical to rectangular
y=rsinθ
3
New cards
Cylindrical to rectangular
z=z
4
New cards
Rectangular to cylindrical
r=√(x²+y²)
5
New cards
Rectangular to cylindrical
θ=tan⁻¹(y/x)
6
New cards
Cylindrical volume element
dV=rdrdθdz
7
New cards
Spherical to rectangular
x=ρsinφcosθ
8
New cards
Spherical to rectangular
y=ρsinφsinθ
9
New cards
Spherical to rectangular
z=ρcosφ
10
New cards
Rectangular to spherical
ρ=√(x²+y²+z²)
11
New cards
Rectangular to spherical
θ=tan⁻¹(y/x)
12
New cards
Rectangular to spherical
φ=cos⁻¹(z/ρ)
13
New cards
Spherical volume element
dV=ρ²sinφ dρ dφ dθ
14
New cards
Meaning of r
Distance from z-axis.
15
New cards
Meaning of ρ
Distance from origin.
16
New cards
Meaning of φ
Angle down from positive z-axis.
17
New cards
Meaning of θ
Angle in xy-plane.
18
New cards
When to use cylindrical
Cylinders, circles, symmetry around z-axis.
19
New cards
When to use spherical
Spheres, cones, symmetry about origin.
20
New cards
Common mistake
Mixing up φ and θ.
21
New cards
Exam shortcut
Draw a quick sketch before converting coordinates.