Originally Posted by

**Mush** If this is supposed to be the dot product of two vectors $\displaystyle (\cos(\theta), \sin(\theta)) $ and $\displaystyle (\cos(\theta + 90), \sin(\theta + 90)) $, then:

$\displaystyle (\cos(\theta), \sin(\theta)) \cdot (\cos(\theta + 90), \sin(\theta + 90)) $$\displaystyle = \cos(\theta)\times\cos(\theta + 90)+sin(\theta)\times \sin(\theta + 90)$

$\displaystyle = \cos(\theta)(\cos(\theta)\cos(90)-\sin(\theta)\sin(90))+sin(\theta)( \sin(\theta)\cos(90) + \sin(90)\cos(\theta))$

Since $\displaystyle \sin(90) = 1$ and $\displaystyle \cos(90) = 0 $:

$\displaystyle = \cos(\theta)(-\sin(\theta))+sin(\theta)\cos(\theta) $

$\displaystyle = -\cos(\theta)\sin(\theta)+sin(\theta)\cos(\theta) = 0$

You should expect this result, since the 2nd vector is the same as the first vector, except it has been rotated through and angle of 90 degrees, and is hence perpendicular. And the dot product of two perpendicular vectors is always 0.