Convert the point with cylindrical coordinates 11π 13, 5 to Cartesian coordinates. Enter your answer 9 6 as an ordered triple using exact values involving radicals as necessary. (x, y, z)
Convert the point with cylindrical coordinates 11π 13, 5 to Cartesian coordinates. Enter your answer 9 6 as an ordered triple using exact values involving radicals as necessary. (x, y, z)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Converting Cylindrical to Cartesian Coordinates**
**Problem:**
Convert the point with cylindrical coordinates \((13, \frac{11\pi}{6}, 5)\) to Cartesian coordinates. Enter your answer as an ordered triple using exact values involving radicals as necessary.
\((x, y, z) = \) [Blank Box for Answer]
**Explanation:**
To convert from cylindrical coordinates \((r, \theta, z)\) to Cartesian coordinates \((x, y, z)\), use the following formulas:
1. \(x = r \cdot \cos(\theta)\)
2. \(y = r \cdot \sin(\theta)\)
3. \(z = z\)
Given:
- \(r = 13\)
- \(\theta = \frac{11\pi}{6}\)
- \(z = 5\)
Plug these values into the formulas to find the Cartesian coordinates.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4e39a1d0-143c-41f0-ae59-e967e0535bad%2F1f812e46-c8dc-466c-b1a1-f40b78b258e4%2Fj9rkhm9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Converting Cylindrical to Cartesian Coordinates**
**Problem:**
Convert the point with cylindrical coordinates \((13, \frac{11\pi}{6}, 5)\) to Cartesian coordinates. Enter your answer as an ordered triple using exact values involving radicals as necessary.
\((x, y, z) = \) [Blank Box for Answer]
**Explanation:**
To convert from cylindrical coordinates \((r, \theta, z)\) to Cartesian coordinates \((x, y, z)\), use the following formulas:
1. \(x = r \cdot \cos(\theta)\)
2. \(y = r \cdot \sin(\theta)\)
3. \(z = z\)
Given:
- \(r = 13\)
- \(\theta = \frac{11\pi}{6}\)
- \(z = 5\)
Plug these values into the formulas to find the Cartesian coordinates.
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