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# Transformation Matrices (Rotation matrix)- I just dont get it! watch

1. Hi guys,

I'm revising for my MEI FP1 Exam and I just dont get how the rotation matrix works:

I know the following:

The transformation matrix
(cos x -sin x)
(sin x cos x)

represents a rotation through angle x anticlockwise about the origin.

What I dont get is the following:
-Is it in degrees or radians?
- Given some decimals in that form, how do you work out the angle of rotation and which direction?
2. (Original post by Eux)
Hi guys,

I'm revising for my MEI FP1 Exam and I just dont get how the rotation matrix works:

I know the following:

The transformation matrix
(cos x -sin x)
(sin x cos x)

represents a rotation through angle x anticlockwise about the origin.

What I dont get is the following:
-Is it in degrees or radians?
- Given some decimals in that form, how do you work out the angle of rotation and which direction?
If they ask you what tranformation is given by a specific matrix, just do the following:

1 Look at the signs of the matrix given. If the signs alternate in the same way as the rotation matrix, then you know its a rotation.

3. Then equate the various parts of the matrices correspondingly, to solve for theta. Then the value of theta is the angle by which the point has been rotated anticlockwise.

Remember, if the sign of theta is negative, the rotation is clockwise.
3. (Original post by Xin Xang)
If they ask you what tranformation is given by a specific matrix, just do the following:

1 Look at the signs of the matrix given. If the signs alternate in the same way as the rotation matrix, then you know its a rotation.

3. Then equate the various parts of the matrices correspondingly, to solve for theta. Then the value of theta is the angle by which the point has been rotated anticlockwise.

Remember, if the sign of theta is negative, the rotation is clockwise.
What happens if arccos x and arcsin x where x is the angle in radians, are different to each other?
4. (Original post by Eux)
What happens if arccos x and arcsin x where x is the angle in radians, are different to each other?
Then its not a rotation. But if the signs are all fine, then it almost always will be a rotation. The first thing you should check is the signs. If the signs are fine, you have probably made a calculation error.

Edit: I should also mention that by signs I mean that the matrix should go like;

Top left: x
Top right: y
Bottom left:-y
Bottom right: x

if that makes any sense.

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Updated: May 10, 2015
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