Explanation Given: r = 2 sin θ Calculation: The objective is to convert the given polar form in an equation in rectangular form. Polar coordinates of a given point are in the form of ( r , θ ) where r is the distance of the point from origin and θ is the angle measured from positive x − a x i s to that point. The rectangular coordinates are represented as ( x , y ) where x is the horizontal distance of the point and y is the vertical distance. The relation between the rectangular and polar coordinates is x = r cos θ y = r sin θ Squaring and adding the above equation you get the equation in rectangular form as: x 2 + y 2 = r 2 The relation between rectangular and polar coordinates can be shown on a right angled triangle as: From the relation you have: y = r sin θ y r = sin θ Put this value of sin θ in the given relation r = 2 sin θ ...

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 12.3, Problem 15E

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An equation in rectangular coordinates.

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Chapter 12.3, Problem 14E

Chapter 12.3, Problem 16E

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Chapter 12 Solutions

CALCULUS W/SAPLING ACCESS >IC<

Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 7PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

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An equation in rectangular coordinates.

Solution Summary: The author explains that the equation in rectangular coordinates is x 2 + (y 1) 2 = 1.

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An equation in rectangular coordinates.

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