Different rotation matrix, with cosine?

1. Sep 10, 2011

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.

2. Sep 10, 2011

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.