Graph of the tangent

The tangent too is represented on a Cartesian plane, but its graph looks very different from that of sine and cosine.

One branch of the graph of $\tan x$, on the interval $\left(-\tfrac{\pi}{2},\tfrac{\pi}{2}\right)$. The branch repeats identically every $\pi$.

The tangent has period $\pi$ (it repeats every half turn). The vertical asymptotes are the lines $x=\tfrac{\pi}{2}+k\pi$ (where $\cos=0$). Between two consecutive asymptotes the function is strictly increasing, passes through zero where $\sin=0$, and tends to $\pm\infty$ as $\alpha$ approaches the value where $\cos$ changes sign.

Links

Topics: Trigonometry
Concepts: Asymptote · Periodicity · Tangent
Functions: Tangent
Skills: Interpreting a graph · Drawing a graph