anonymous
  • anonymous
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?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
I just wrote a huge piece and this site kiboshed what I wrote. Did you get anything for this question?
anonymous
  • 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 \[\cos \theta =-\frac{1}{\sqrt{2}}\]
anonymous
  • anonymous
In one rotation, \[\sin \theta = -\frac{1}{\sqrt{2}} \rightarrow \theta =225^o, 315^o\]

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anonymous
  • anonymous
\[\cos \theta = -\frac{1}{\sqrt{2}} \rightarrow \theta = 135^o, 225^o\]
anonymous
  • 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.

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