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I can easily rotate sprites using the Draw method. However I would like to simply rotate a Rectangle (the structure) so that I can get the coordinate of the four corners of the rectangle. How can I do that?

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You can't rotate a Microsoft.Xna.Framework.Rectangle. It is by nature an axis aligned structure only.

What do you hope to do with the corners that you want to find? Maybe we could suggest a good way to accomplish your goal.

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You can make for all 4 points something like this:

public static Vector2 RotateAround(this Vector2 source, Vector2 target, float radians)
 Vector2 fromAround = source - target;
 float postRotationX = (float)(fromAround.X * Math.Cos(radians) - fromAround.Y * Math.Sin(radians));
 float postRotationY = (float)(fromAround.X * Math.Sin(radians) - fromAround.Y * Math.Cos(radians));
 return target + new Vector2(postRotationX, postRotationY);

Code From MSDN

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Pretty sure that rotation should have a + before the Y * cos term. – Andrew Russell Jun 17 '11 at 1:32

If you want to get the coordinates of the rotated corners, you have to transform the coordinates from the non-rotated space to the rotated space. In other words, you have to multiply them by a matrix. I'm not sure the exact xna syntax, but it should be something like this:

float angle = 60;
Matrix rotate = Matrix.CreateRotationZ(angle);    
Vector2 transformedPoint = Vector2.Transform(unTransformedPoint, rotate);

This will rotate the rectangle about it's top left corner. I'm not sure if that's what you want or not, but you can easily change this by adding a translate transform before the rotate transform to change the rotation origin.

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