anonymous 5 years ago If the rotation matrix in the rotation equation is matrix[x_y]=matrix[-√(2)/2,-√(2)/2,_√(2)/2,-√(2)/2,]*matrix[x'_y']. What angle of rotation is being used?

1. anonymous

I just wrote a huge piece and this site kiboshed what I wrote. Did you get anything for this question?

2. anonymous

Basically, identify the entries in your matrix with each of the trig. functions that describe a rotation matrix in two dimensions. You should have then,$\sin \theta = -\frac{1}{\sqrt{2}}$and $\cos \theta =-\frac{1}{\sqrt{2}}$

3. anonymous

In one rotation, $\sin \theta = -\frac{1}{\sqrt{2}} \rightarrow \theta =225^o, 315^o$

4. anonymous

$\cos \theta = -\frac{1}{\sqrt{2}} \rightarrow \theta = 135^o, 225^o$

5. anonymous

The only angle BOTH trig. functions have in common is 225 degrees. Unless I've misread your matrix entries, this is the angle of rotation.