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(1, √3) (a, b) = (-2, (-2,√3) (2√3, 2) (√3, 1) (√3, -1) - (a, b) - (a, b) = - (a, b) = (-1, √3) (a, b) = (1, -2) (a, b) = (2, 2√√3) - - (a, b) - - (a, b) - = = =

(1, √3) (a, b) = (-2, (-2,√3) (2√3, 2) (√3, 1) (√3, -1) - (a, b) - (a, b) = - (a, b) = (-1, √3) (a, b) = (1, -2) (a, b) = (2, 2√√3) - - (a, b) - - (a, b) - = = =

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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Here is the transcription of the text: 1. \((a, b) = \left(1, \sqrt{3}\right)\) 2. \((a, b) = \left(-2, \sqrt{3}\right)\) 3. \((a, b) = \left(2\sqrt{3}, 2\right)\) 4. \((a, b) = \left(\sqrt{3}, 1\right)\) 5. \((a, b) = \left(\sqrt{3}, -1\right)\) 6. \((a, b) = \left(-1, \sqrt{3}\right)\) 7. \((a, b) = \left(1, -2\right)\) 8. \((a, b) = \left(2, 2\sqrt{3}\right)\) This list comprises ordered pairs \((a, b)\) where each value is either an integer or involves the square root of 3.
Transcribed Image Text:Here is the transcription of the text: 1. \((a, b) = \left(1, \sqrt{3}\right)\) 2. \((a, b) = \left(-2, \sqrt{3}\right)\) 3. \((a, b) = \left(2\sqrt{3}, 2\right)\) 4. \((a, b) = \left(\sqrt{3}, 1\right)\) 5. \((a, b) = \left(\sqrt{3}, -1\right)\) 6. \((a, b) = \left(-1, \sqrt{3}\right)\) 7. \((a, b) = \left(1, -2\right)\) 8. \((a, b) = \left(2, 2\sqrt{3}\right)\) This list comprises ordered pairs \((a, b)\) where each value is either an integer or involves the square root of 3.
**Problem Statement:** Find the Cartesian coordinates, \((a, b)\), of the point given in polar coordinates by \(P(2, \pi/3)\). **Explanation:** In this problem, you are asked to convert polar coordinates to Cartesian coordinates. The polar coordinates are given as \(P(2, \pi/3)\), where 2 is the radius \(r\) and \(\pi/3\) is the angle \(\theta\). To convert from polar coordinates \((r, \theta)\) to Cartesian coordinates \((x, y)\), the following formulas are used: \[ x = r \cdot \cos(\theta) \] \[ y = r \cdot \sin(\theta) \] **Solution Steps:** 1. Identify the given polar coordinates: \(r = 2\), \(\theta = \pi/3\). 2. Calculate the Cartesian coordinate \(x\): \[ x = 2 \cdot \cos(\pi/3) \] 3. Calculate the Cartesian coordinate \(y\): \[ y = 2 \cdot \sin(\pi/3) \] Using these calculations, you will find the Cartesian coordinates \((a, b)\) of the given point.
Transcribed Image Text:**Problem Statement:** Find the Cartesian coordinates, \((a, b)\), of the point given in polar coordinates by \(P(2, \pi/3)\). **Explanation:** In this problem, you are asked to convert polar coordinates to Cartesian coordinates. The polar coordinates are given as \(P(2, \pi/3)\), where 2 is the radius \(r\) and \(\pi/3\) is the angle \(\theta\). To convert from polar coordinates \((r, \theta)\) to Cartesian coordinates \((x, y)\), the following formulas are used: \[ x = r \cdot \cos(\theta) \] \[ y = r \cdot \sin(\theta) \] **Solution Steps:** 1. Identify the given polar coordinates: \(r = 2\), \(\theta = \pi/3\). 2. Calculate the Cartesian coordinate \(x\): \[ x = 2 \cdot \cos(\pi/3) \] 3. Calculate the Cartesian coordinate \(y\): \[ y = 2 \cdot \sin(\pi/3) \] Using these calculations, you will find the Cartesian coordinates \((a, b)\) of the given point.
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