Convert the point (p, 0, 6) = answers either as expressions, (x, y, z) = 5π 2π to Cartesian coordinates. Give 9 4 3 or decimals to at least one decimal place. 3,
Convert the point (p, 0, 6) = answers either as expressions, (x, y, z) = 5π 2π to Cartesian coordinates. Give 9 4 3 or decimals to at least one decimal place. 3,
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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2.7.6
![**Convert the Point from Spherical to Cartesian Coordinates**
---
**Problem Statement:**
Convert the point \((\rho, \theta, \phi) = \left(3, \frac{5\pi}{4}, \frac{2\pi}{3}\right)\) to Cartesian coordinates. Provide answers either as expressions, or decimals to at least one decimal place.
\[
(x, y, z) = \text{__________}
\]
---
**Explanation:**
To convert from spherical to Cartesian coordinates, use the following formulas:
- \(x = \rho \cdot \sin(\phi) \cdot \cos(\theta)\)
- \(y = \rho \cdot \sin(\phi) \cdot \sin(\theta)\)
- \(z = \rho \cdot \cos(\phi)\)
Given:
- \(\rho = 3\)
- \(\theta = \frac{5\pi}{4}\)
- \(\phi = \frac{2\pi}{3}\)
Substitute these values into the formulas to find \(x\), \(y\), and \(z\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F21e8a523-579f-40b9-8f0a-805524283a8d%2Fa333251a-47cc-4e09-9634-4f9ea5e3d86b%2F0u6eg8u_processed.png&w=3840&q=75)
Transcribed Image Text:**Convert the Point from Spherical to Cartesian Coordinates**
---
**Problem Statement:**
Convert the point \((\rho, \theta, \phi) = \left(3, \frac{5\pi}{4}, \frac{2\pi}{3}\right)\) to Cartesian coordinates. Provide answers either as expressions, or decimals to at least one decimal place.
\[
(x, y, z) = \text{__________}
\]
---
**Explanation:**
To convert from spherical to Cartesian coordinates, use the following formulas:
- \(x = \rho \cdot \sin(\phi) \cdot \cos(\theta)\)
- \(y = \rho \cdot \sin(\phi) \cdot \sin(\theta)\)
- \(z = \rho \cdot \cos(\phi)\)
Given:
- \(\rho = 3\)
- \(\theta = \frac{5\pi}{4}\)
- \(\phi = \frac{2\pi}{3}\)
Substitute these values into the formulas to find \(x\), \(y\), and \(z\).
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