1) Express in cylindrical and spherical coordinate systems. Cylindrical Spherical Coordinates Coordinates The XZ plane The Y axis The Z axis The line Y = X on the XY plane The plane Y = X Ray X=Y=Z in 1st octant Ray X=Y=Z in 7th octant Circle X² + Y²=C² on XY plane The sphere X² + y² + Z² = C² Equator of sphere x² + y² + Z² = C² South Pole of the sphere x² + y² + Z² = C²
1) Express in cylindrical and spherical coordinate systems. Cylindrical Spherical Coordinates Coordinates The XZ plane The Y axis The Z axis The line Y = X on the XY plane The plane Y = X Ray X=Y=Z in 1st octant Ray X=Y=Z in 7th octant Circle X² + Y²=C² on XY plane The sphere X² + y² + Z² = C² Equator of sphere x² + y² + Z² = C² South Pole of the sphere x² + y² + Z² = C²
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:**Title: Understanding Fractions in Cylindrical and Spherical Coordinate Systems**
### Problem Statement
1. **Express in Cylindrical and Spherical Coordinate Systems.**
| | **Cylindrical Coordinates** | **Spherical Coordinates** |
|-------------------------------|-----------------------------|---------------------------|
| The XZ plane | | |
| The Y axis | | |
| The Z axis | | |
| The line Y = X on the XY plane| | |
| The plane Y = X | | |
| Ray X = Y = Z in 1st octant | | |
| Ray X = Y = Z in 7th octant | | |
| Circle X² + Y² = C² on XY plane | | |
| The sphere X² + Y² + Z² = C² | | |
| Equator of sphere | | |
| X² + Y² + Z² = C² | | |
| South Pole of the sphere | | |
| X² + Y² + Z² = C² | | |
### Explanation
In this table, there are geometric entities that you need to express using both cylindrical and spherical coordinates. The expressions for cylindrical and spherical coordinates are left blank for you to fill in. Below is a brief guide on how to approach this:
- **Cylindrical Coordinates:**
- Defined by (ρ, φ, z) where ρ is the radial distance, φ is the azimuthal angle, and z is the height.
- **Spherical Coordinates:**
- Defined by (r, θ, φ) where r is the radial distance from the origin, θ is the polar angle, and φ is the azimuthal angle.
Use this guide to help convert the given scenarios into the appropriate coordinate systems.
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