Tangent and its breaks

Tangent repeats after \(180^\circ\). It is zero at \(0^\circ,180^\circ,360^\circ\), and undefined at \(90^\circ,270^\circ\). Draw separate increasing branches and dashed vertical asymptotes at the undefined angles.

For example, \(\tan45^\circ=\tan225^\circ=1\). There is no maximum or minimum: each complete branch increases without bound near its asymptotes. Never join across a break.