From Förberedande kurs i matematik 1

If we draw the angle \displaystyle {\pi }/{5}\; on a unit circle, then it will have an \displaystyle x -coordinate that is equal to \displaystyle {\cos \pi }/{5}\;

the line \displaystyle x={\cos \pi }/{5}\;

In the figures, we see also that the only other angle between $0\; and$\displaystyle 2\pi which has the same cosine value, i.e. same \displaystyle x -coordinate, is the angle \displaystyle v=-\frac{\pi }{5}+2\pi =\frac{9\pi }{5} on the opposite side of the \displaystyle x -axis.