### Polar to Cartesian Coordinates ConversionThis educational material focuses on converting polar coordinates to Cartesian coordinates, complete with visual graph representations.#### Question (b)**Given Polar Coordinates:**\[ \left( 3\sqrt{2}, \frac{\pi}{4} \right) \]You are provided with four graphs labeled as Choice A, B, C, and D, each displaying a Cartesian plane with a plotted point. Your task is to identify which graph correctly represents the Cartesian conversion of the given polar coordinates.The graphs have the following properties:- Each graph contains x and y axes ranging from -4 to 4.- A specific point is plotted in each graph indicating its (x, y) position.**Explanation of the Graphs:**1. **Choice A:** - The point is plotted at approximately \((-2, -2)\).2. **Choice B:** - The point is plotted at approximately \((3, 0)\).3. **Choice C:** - The point is plotted at approximately \((2, 2)\).4. **Choice D:** - The point is plotted at approximately \((0, 3)\).**Conversion Formula:**To convert from polar (\(r, \theta\)) to Cartesian (\(x, y\)) coordinates:- \(x = r \cdot \cos(\theta)\)- \(y = r \cdot \sin(\theta)\)Applying the conversion:- \(r = 3\sqrt{2}\)- \(\theta = \frac{\pi}{4}\)Calculate:- \(x = 3\sqrt{2} \cdot \cos\left(\frac{\pi}{4}\right) = 3\sqrt{2} \cdot \frac{\sqrt{2}}{2} = 3\)- \(y = 3\sqrt{2} \cdot \sin\left(\frac{\pi}{4}\right) = 3\sqrt{2} \cdot \frac{\sqrt{2}}{2} = 3\)Thus, the correct Cartesian coordinates are \((3, 3)\).Using this information, select the correct graph.#### (x, y) = \((\_\_\_)\)#### Question (c)**Given Polar Coordinates:**\[ \left( -5, -\frac{\ **Title: Conversion of Polar Coordinates to Cartesian Coordinates****Objective:**Plot the point defined by polar coordinates and find its Cartesian coordinates.**Problem Statement:**Given polar coordinates \( (3, \frac{3\pi}{2}) \), plot the point and determine its Cartesian coordinates.**Graphical Representation:**Four options labeled as Choice A, B, C, and D are provided, each with a distinct point plotted on a Cartesian coordinate system.1. **Choice A:** Point is at \((-3, 0)\).2. **Choice B:** Point is at \((0, -3)\).3. **Choice C:** Point is at \((0, 3)\).4. **Choice D:** Point is at \((3, 0)\).**Conversion Formula:**To convert from polar coordinates \((r, \theta)\) to Cartesian coordinates \((x, y)\):- \( x = r \cos \theta \)- \( y = r \sin \theta \)**Solution Steps:**1. **Calculate Cartesian Coordinates:** - Given: \( r = 3 \), \( \theta = \frac{3\pi}{2} \) - \( x = 3 \cos \frac{3\pi}{2} = 3 \times 0 = 0 \) - \( y = 3 \sin \frac{3\pi}{2} = 3 \times (-1) = -3 \)2. **Identify Correct Choice:** - The correct Cartesian coordinates are \( (0, -3) \), which corresponds to Choice B.**Final Answer:**\( (x, y) = (0, -3) \)This exercise aids in understanding the relationship between polar and Cartesian coordinate systems by practicing conversions and plotting points accurately.

Answered: Image /qna-images/answer/1a541395-1b9a-4be7-9132-b3b813c07ca2.jpg

Answered: Plot the point whose polar coordinates…

Plot the point whose polar coordinates are given. Then find the Cartesian coordinates of the point. (0) (3, 2) CHOICE A

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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