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(r, 0) 4, – 3+ 27 (r > 0) %3D

(r, 0) 4, – 3+ 27 (r > 0) %3D

Calculus: Early Transcendentals
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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What would be the Cartesian point?

The polar coordinate is given by \((r, \theta) = \left(4, -3 + 2\pi\right)\) with \(r > 0\). This expression represents a point in polar coordinates, where \(r\) is the radial distance from the origin, and \(\theta\) is the angular coordinate. The angle \(-3 + 2\pi\) demonstrates an adjustment in the angle measure, and due to the addition of \(2\pi\), it's equivalent to rotating by \(360^\circ\), which can help in finding a positive equivalent angle. The radial distance \(r\) is positive, indicating the point lies on the same radial line as \((4, -3)\), but adjusted to fit the standard form by adding \(2\pi\). The green check mark indicates that these coordinates satisfy the condition \(r > 0\).
Transcribed Image Text:The polar coordinate is given by \((r, \theta) = \left(4, -3 + 2\pi\right)\) with \(r > 0\). This expression represents a point in polar coordinates, where \(r\) is the radial distance from the origin, and \(\theta\) is the angular coordinate. The angle \(-3 + 2\pi\) demonstrates an adjustment in the angle measure, and due to the addition of \(2\pi\), it's equivalent to rotating by \(360^\circ\), which can help in finding a positive equivalent angle. The radial distance \(r\) is positive, indicating the point lies on the same radial line as \((4, -3)\), but adjusted to fit the standard form by adding \(2\pi\). The green check mark indicates that these coordinates satisfy the condition \(r > 0\).
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