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Plot the point whose spherical coordinates are given. Then find the rectangular coordinates of the point. 3π (a) (8, 34, 7/7) 2 (x, y, z) = (b) (7₁-7) 3 4 (x, y, z) = (

Plot the point whose spherical coordinates are given. Then find the rectangular coordinates of the point. 3π (a) (8, 34, 7/7) 2 (x, y, z) = (b) (7₁-7) 3 4 (x, y, z) = (

Advanced Engineering Mathematics
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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Plot the point whose spherical coordinates are given. Then find the rectangular coordinates of the point.

(a)

 
8, 
3?
4
, 
?
2
 
(x, y, z) = 
 
 
 
 
 
 
 

(b)

 
7, − 
?
3
, 
?
4
 
(x, y, z) = 
 
 
 
 
 
 
 
**Text from the Image:** Plot the point whose spherical coordinates are given. Then find the rectangular coordinates of the point. (a) \(\left( 8, \frac{3\pi}{4}, \frac{\pi}{2} \right)\) \((x, y, z) = \left( \text{\_\_\_\_\_\_\_\_} \right)\) (b) \(\left( 7, -\frac{\pi}{3}, \frac{\pi}{4} \right)\) \((x, y, z) = \left( \text{\_\_\_\_\_\_\_\_} \right)\) **Explanation for Students:** In these exercises, you need to convert the given spherical coordinates to rectangular coordinates. Spherical coordinates are represented as \((rho, theta, phi)\): - \(rho\) (ρ) is the radial distance from the origin. - \(theta\) (θ) is the angle in the xy-plane from the positive x-axis. - \(phi\) (φ) is the angle from the positive z-axis. To convert these to rectangular coordinates \((x, y, z)\), you can use the formulas: - \(x = rho \cdot \sin(phi) \cdot \cos(theta)\) - \(y = rho \cdot \sin(phi) \cdot \sin(theta)\) - \(z = rho \cdot \cos(phi)\) Use these formulas to calculate the rectangular coordinates for parts (a) and (b).
Transcribed Image Text:**Text from the Image:** Plot the point whose spherical coordinates are given. Then find the rectangular coordinates of the point. (a) \(\left( 8, \frac{3\pi}{4}, \frac{\pi}{2} \right)\) \((x, y, z) = \left( \text{\_\_\_\_\_\_\_\_} \right)\) (b) \(\left( 7, -\frac{\pi}{3}, \frac{\pi}{4} \right)\) \((x, y, z) = \left( \text{\_\_\_\_\_\_\_\_} \right)\) **Explanation for Students:** In these exercises, you need to convert the given spherical coordinates to rectangular coordinates. Spherical coordinates are represented as \((rho, theta, phi)\): - \(rho\) (ρ) is the radial distance from the origin. - \(theta\) (θ) is the angle in the xy-plane from the positive x-axis. - \(phi\) (φ) is the angle from the positive z-axis. To convert these to rectangular coordinates \((x, y, z)\), you can use the formulas: - \(x = rho \cdot \sin(phi) \cdot \cos(theta)\) - \(y = rho \cdot \sin(phi) \cdot \sin(theta)\) - \(z = rho \cdot \cos(phi)\) Use these formulas to calculate the rectangular coordinates for parts (a) and (b).
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