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

waigaK

waigaK

Answered question

2020-11-17

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

Answer & Explanation

lamanocornudaW

lamanocornudaW

Skilled2020-11-18Added 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.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Linear algebra

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?