Aus Online Mathematik Brückenkurs 1

If we write the angle \displaystyle \frac{7\pi }{5} as

\displaystyle \frac{7\pi}{5} = \frac{5\pi+2\pi}{5} = \pi + \frac{2\pi }{5}

we see that \displaystyle 7\pi/5 is an angle in the third quadrant.

The angle between \displaystyle 0 and \displaystyle \pi which has the same x-coordinate as the angle \displaystyle 7\pi/5, and hence the same cosine value, is the reflection of the angle \displaystyle 7\pi/5 in the x-axis, i.e.

\displaystyle v = \pi -\frac{2\pi}{5} = \frac{3\pi}{5}\,\textrm{.}