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We have a rectangle that is rotating by its center from $0$ to $360$ degrees. This rectangle rotation starts in $0$ degrees when we know all four rectangle points. We also know the angle we want to rotate the rectangle.

What I need is a formula for these points when rectangle is rotated.

Picture

hardmath
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    Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. – José Carlos Santos Dec 26 '17 at 19:09
  • For example, you might explain how you can accomplish this for rectangles centered on the origin. Readers can then show you how to relate that to rectangles centered on arbitrary points. – hardmath Dec 26 '17 at 20:10

1 Answers1

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When you rotate the point $(x,y)$ through an angle of $\theta$ (radians, not degrees) about the origin the new position is $$ (x \cos\theta - y \sin\theta\ , \quad x\sin\theta + y\cos\theta). $$

(https://en.wikipedia.org/wiki/Rotation_matrix)

If the center of the rectangle is not at the origin, translate the center to move it there, rotate, then translate back.

Ethan Bolker
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