Explanation Result used: (1) To find a rotation through a positive acute angle θ , use the equations x = x ′ cos θ − y ′ sin θ and y = x ′ sin θ + y ′ cos θ . (2) Identify a conic section form the value of B 2 − 4 A C . “1. B 2 − 4 A C = 0 , a parabola . 2. B 2 − 4 A C < 0 , an ellipse . 3. B 2 − 4 A C > 0 , a hyperbola ”. Calculation: The given line equation is y = x and the angle is θ = 45 ° . Obtain the rotation equations. Substitute θ = 45 ° in x = x ′ cos θ − y ′ sin θ . x = x ′ cos 45 ° − y ′ sin 45 ° = x ′ 2 − y ′ 2 Substitute θ = 45 ° in y = x ′ sin θ + y ′ cos θ

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 21.9, Problem 24E

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The x′y′ equation of the line y=x when the axes are rotated through 45°.

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Chapter 21.9, Problem 23E

Chapter 21.9, Problem 25E

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Chapter 21 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 21.1 - Find the distance between (−2, 6) and (5, −3). Ch. 21.1 - Prob. 2PE Ch. 21.1 - Prob. 1E Ch. 21.1 - Prob. 2E Ch. 21.1 - Prob. 5E Ch. 21.1 - In Exercises 5–14, find the distance between the...Ch. 21.1 - Prob. 7E Ch. 21.1 - Prob. 8E Ch. 21.1 - Prob. 9E Ch. 21.1 - Prob. 10E

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The x ′ y ′ equation of the line y = x when the axes are rotated through 45 ° .

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The x′y′ equation of the line y=x when the axes are rotated through 45°.

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Chapter 21 Solutions