How Do You Determine the Angle of Rotation from a 2x2 Matrix?

[Natasha1]

I just wanted to know how I could work out the angle of rotation from the following matrix -0.6, -0.8 (top) and 0.8, -0.6 (bottom)?

Is this possible or am I missing something here?

 

[matt grime]

Rotation matrices have a certain form (cos, sin, -sin, cos) or something. You can do inverse sin, or cos, so all is well.

 

[Natasha1]

right,

so I get:

a (top left of matrix) => cos-1 (-0.6) = 126.9 degrees

b (top right of matrix) => -sin-1 (-0.8) = 53.1 degrees

c (bottom left of matrix) => sin-1 (0.8) = 53.1 degrees

d (bottom right of matrix) => cos-1 (-0.6) = 126.9 degrees

What is the overall transformation? Is is 126.9 + 53.1 = 180 degrees?

 

[finchie_88]

It can't be 180 degrees, since that would give you a matrix of (-1, 0 , 0, -1), in the order, top left, top right, bottom left and bottom right, i think. I think that the angle of rotation from the positive x-axis is 126.9 degrees, but I'm not entirely sure.

 

[matt grime]

It's either 123.9 or 56.1 (and of course they add up to 180), check the correct form of a rotation matrix in your notes.