Tangent, curve of the

The graph of the function (Fig.a). The curve of the tangent is a periodic curve with period and asymptotes , . While varies from to , grows monotonically from to ; thus, the curve of the tangent is composed of infinitely many separate congruent curves obtained from one another by translation over along the -axis. The points of intersection with the -axis are . These are also the points of inflection, with inclination angle to the -axis.

Figure: t092130a

The curve of the tangent reflected mirror-like in the -axis and translated to the left over (Fig.b) becomes the graph of the function (cf. Cotangent); its asymptotes are ; its intersections with the -axis are and these points are also the points of inflection, with inclination angle with respect to the -axis.

Figure: t092130b