From Förberedande kurs i matematik 1

In order to get an angle between \displaystyle 0 and \displaystyle \text{2}\pi , we subtract \displaystyle \text{2}\pi from \displaystyle {7\pi }/{2}\; , which also leaves the cosine value unchanged

\displaystyle \cos \frac{7\pi }{2}=\cos \left( \frac{7\pi }{2}-2\pi \right)=\cos \frac{3\pi }{2}

When we draw a line which makes an angle \displaystyle {3\pi }/{2}\; with the positive \displaystyle x -axis, we get the negative \displaystyle y -axis and we see that this line cuts the unit circle at the point \displaystyle \left( 0 \right.,\left. -1 \right). The \displaystyle x -coordinate of the intersection point is thus \displaystyle 0 and hence \displaystyle \cos {7\pi }/{2}\;=\cos {3\pi }/{2}\;=0