The coordinates of the point in the x^{prime} y^{prime} - coordinate system with the given angle of rotation and the xy-coordinates.

waigaK 2020-11-17 Answered

The coordinates of the point in the x' y' - coordinate system with the given angle of rotation and the xy-coordinates.

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Expert Answer

lamanocornudaW
Answered 2020-11-18 Author has 85 answers

Suppose the x- and y- axes are rotated about the origin through a positive acute angle θ, then the coordinates (x, y) and (x,y) of a point P in the xy- and x,y- coordinate systems are related by the following formulas:
x=xcosθ + ysinθ
y= xsinθ + ycosθ
x=xcosθ  ysinθ
y=xsinθ + ycosθ
Given:
The angle of rotation is θ=30 and the x- and y- coordinates are 0 and 2, respectively.
Calculation:
Use the definition, substitute the values of x-, y- coordinates and θ in order to obtain the values of x, y - coordinates.
x=(0)cos 30 + (2)sin 30
y= (0)sin 30 + (2)cos 30
Know that sin 30=12 and 30=32
Thus, the x and y - coordinates become x=(0) (32) + (2)(12)
=0 + (1)
=1
y= (0)(12) + (2)(32)
=0 + (3)
=3
Therefore, the coordinates of the point the xy - coordinate system are 1 and 3, respectively.

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