From Förberedande kurs i matematik 1

Because \displaystyle \tan v = \frac{\sin v}{\cos v}, the condition \displaystyle \tan v = 1 gives \displaystyle \sin v = \cos v, i.e. we look for angles in the unit circle whose x- and y-coordinates are equal.

After drawing the unit circle and the line y=x, we see that there are two angles which satisfy these conditions, \displaystyle v=\pi/4 and \displaystyle v = \pi + \pi/4 = 5\pi/4\,.