Explanation Calculation: Consider the provided coordinates of the point in x y -coordinate system. x , y = 4 , 1 Now, consider the angle of rotation θ for the x ′ y ′ -coordinate system. θ = 90 ° The relationship between the coordinates of x y -coordinate system and x ′ y ′ -coordinate system is: x = x ′ c o s θ − y ′ s i n θ y = x ′ sin θ + y ′ cos θ Now, substitute the provided coordinates x , y = 4 , 1 and the angle of rotation θ = 90 ° in the above relation. 4 = x ′ cos 90 ° − y ′ sin 90 ° ...... 1 And, 1 = x ′ s i n 90 ° + y ′ c o s 90 °

Bundle: Trigonometry, 10th + Webassign Printed Access Card For Larson's Trigonometry, 10th Edition, Single-term

10th Edition

ISBN: 9781337605175

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 6E

To determine

To calculate: The coordinates of the point 4,1 from the xy -coordinate system in the new rotated x′y′ -coordinate system, where the angle of rotation θ=90°.

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Chapter 6.5, Problem 5E

Chapter 6.5, Problem 7E

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Chapter 6 Solutions

Bundle: Trigonometry, 10th + Webassign Printed Access Card For Larson's Trigonometry, 10th Edition, Single-term

Ch. 6.1 - Find the inclination of (a) 4x5y=7 and (b) x+y=1.Ch. 6.1 - Prob. 2ECP Ch. 6.1 - Prob. 3ECP Ch. 6.1 - Find the distance between the point 3,2 and the...Ch. 6.1 - Prob. 5ECP Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E

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The coordinates of the point 4 , 1 from the x y - coordinate system in the new rotated x ′ y ′ -coordinate system, where the angle of rotation θ = 90 ° .

Solution Summary: The author calculates the coordinates of the given point in the xy -coordinate system.

To calculate: The coordinates of the point 4,1 from the xy -coordinate system in the new rotated x′y′ -coordinate system, where the angle of rotation θ=90°.

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Chapter 6 Solutions