Aus Online Mathematik Brückenkurs 1

The angle \displaystyle \pi/2+v makes the same angle with the positive y-axis as the angle v makes with the positive x-axis, and hence we see that the x-coordinate for \displaystyle \pi/2+v is equal to the y-coordinate for v, but with a change of sign, i.e.

\displaystyle \cos \Bigl(\frac{\pi}{2}+v\Bigr) = -\sin v = -a\,\textrm{.}

Angle v	Angle π/2 + v