Different rotation matrix, with cosine?

[vicjun]

I know that a proper orthogonal rotation matrix in R^{2} has the form


[cos \theta sin \theta
-sin \theta cos \theta]


which would rotate a vector by the angle \theta. However, I have also seen the matrix

[sin \theta cos \theta
-cos \theta sin \theta]

What type of rotation is this? Is it even a rotation matrix? Thank you in advance.

 

[micromass]

Recall that \cos(\frac{\pi}{2}-\theta)=\sin(\theta) and \sin(\frac{\pi}{2}-\theta)=\cos(\theta). So by these identities, your matrix turns into a standard rotation matrix.