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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![### Question 13
#### Convert the polar coordinate \( \left(5, \frac{\pi}{4}\right) \) to Cartesian coordinates.
- \( x = \) [Text Box]
- \( y = \) [Text Box]
This question asks the student to convert a given polar coordinate, \(\left(5, \frac{\pi}{4}\right)\), into Cartesian coordinates. In polar coordinates, the first value, 5, represents the radius (r), and the second value, \(\frac{\pi}{4}\), represents the angle (θ) in radians.
To convert polar coordinates (r, θ) to Cartesian coordinates (x, y), use the equations:
- \( x = r \cos(\theta) \)
- \( y = r \sin(\theta) \)
In this case, r = 5 and θ = \( \frac{\pi}{4} \).
1. Calculate \( x \):
\[ x = 5 \cos\left(\frac{\pi}{4}\right) \]
2. Calculate \( y \):
\[ y = 5 \sin\left(\frac{\pi}{4}\right) \]
Students need to input the values they obtain into the provided text boxes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb1c81f19-6b44-4c48-9f6b-8f6cecd1e5f5%2F7a6e6132-5ff3-4d6b-93f1-9c7e8cdd2ffa%2Fto5rme_processed.png&w=3840&q=75)
Transcribed Image Text:### Question 13
#### Convert the polar coordinate \( \left(5, \frac{\pi}{4}\right) \) to Cartesian coordinates.
- \( x = \) [Text Box]
- \( y = \) [Text Box]
This question asks the student to convert a given polar coordinate, \(\left(5, \frac{\pi}{4}\right)\), into Cartesian coordinates. In polar coordinates, the first value, 5, represents the radius (r), and the second value, \(\frac{\pi}{4}\), represents the angle (θ) in radians.
To convert polar coordinates (r, θ) to Cartesian coordinates (x, y), use the equations:
- \( x = r \cos(\theta) \)
- \( y = r \sin(\theta) \)
In this case, r = 5 and θ = \( \frac{\pi}{4} \).
1. Calculate \( x \):
\[ x = 5 \cos\left(\frac{\pi}{4}\right) \]
2. Calculate \( y \):
\[ y = 5 \sin\left(\frac{\pi}{4}\right) \]
Students need to input the values they obtain into the provided text boxes.
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