Explanation Calculation: Consider the given coordinates of the point in x y -coordinate, x , y = 2 , 1 Now, consider the angle of rotation θ for the x ′ y ′ -coordinate system. θ = 45 ° The relationship between the coordinates of the x y -coordinate system and the x ′ y ′ -coordinate system is: x = x ′ cos θ − y ′ sin θ y = x ′ sin θ + y ′ cos θ Now, substitute the given coordinates x , y = 2 , 1 and the angle of rotation θ = 45 ° in the above relation. 2 = x ′ cos 45 ° − y ′ sin 45 ° ...... (1) And, 1 = x ′ sin 45 ° + y ′ cos 45 ° ...... (2) Now, solve the equation 1 , 2 = x ′ 1 2 − y ′ 1 2 And, x ′ − y ′ = 2 2 ...... (3) Now, solve the equation 2 , 1 = x ′ 1 2 + y ′ 1 2 And, x ′ + y ′ = 2 ...... (4) Now, apply the substitution method in the equations 3 and 4 . Substitute the value x ′ = y ′ + 2 2 from equation 4 into the equation 3

10th Edition

ISBN: 9781337278461

Author: Ron Larson

Publisher: Cengage Learning

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Question

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Chapter 6.5, Problem 9E

To determine

To calculate: The coordinates of the point 2,1 from the xy -coordinate system in the newly rotated x′y′ -coordinate system where the angle of rotation θ=45°.

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Chapter 6.5, Problem 8E

Chapter 6.5, Problem 10E

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Chapter 6 Solutions

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Knowledge Booster

The coordinates of the point 2 , 1 from the x y - coordinate system in the newly rotated x ′ y ′ -coordinate system where the angle of rotation θ = 45 ° .

Solution Summary: The author calculates the coordinates of the point (2,1) in the newly rotated

To calculate: The coordinates of the point 2,1 from the xy -coordinate system in the newly rotated x′y′ -coordinate system where the angle of rotation θ=45°.

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Chapter 6 Solutions