Explanation Calculation: Consider the provided coordinates of the point in x y -coordinate, x , y = 3 , 1 Now, consider the angle of rotation θ for the x ′ y ′ -coordinate system. θ = 60 ° The relationship between the coordinates of x y -coordinate system and x ′ y ′ -coordinate system is: x = x ′ cos θ − y ′ sin θ y = x ′ sin θ + y ′ cos θ Now, substitute the provided coordinates x , y = 3 , 1 and the angle of rotation θ = 60 ° in the above relation. 3 = x ′ cos 60 ° − y ′ sin 60 ° ...... (1) And 1 = x ′ s i n 60 ° + y ′ c o s 60 ° ...... (2) Now, solve equation 1 , 3 = x ′ 1 2 − y ′ 3 2 And, x ′ − 3 y ′ = 6 ...... (3) Now, solve equation 2 , 1 = x ′ 3 2 + y ′ 1 2 And 3 x ′ + y ′ = 2 ...... (4) Now, apply the substitution method in the equations 3 and 4 . Substitute the value x ′ = 6 + 3 y ′ from equation 4 in 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 12E

To determine

To calculate: The coordinates of the point 3,1 from the xy -coordinate system in the new rotated x′y′ -coordinate system where the angle of rotation θ=60°.

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Chapter 6.5, Problem 11E

Chapter 6.5, Problem 13E

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Chapter 6 Solutions

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Knowledge Booster

The coordinates of the point 3 , 1 from the x y - coordinate system in the new rotated x ′ y ′ -coordinate system where the angle of rotation θ = 60 ° .

Solution Summary: The author calculates the coordinates of the point (3,1) in the rotated

To calculate: The coordinates of the point 3,1 from the xy -coordinate system in the new rotated x′y′ -coordinate system where the angle of rotation θ=60°.

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Chapter 6 Solutions