From Förberedande kurs i matematik 1

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

\displaystyle \cos \left( \frac{\pi }{2}+v \right)=-\sin v=-a

angle \displaystyle v angle \displaystyle \frac{\pi }{2}+v