Trigonometry/Graphs of Other Trigonometric Functions

A graph of ${\displaystyle \tan(x)}$. ${\displaystyle \tan(x)}$ is defined as ${\displaystyle {\frac {\sin(x)}{\cos(x)}}}$.

A graph of ${\displaystyle \csc(x)}$ . ${\displaystyle \csc(x)}$ is defined as ${\displaystyle {\frac {1}{\sin(x)}}}$ .

A graph of ${\displaystyle \sec(x)}$ . ${\displaystyle \sec(x)}$ is defined as ${\displaystyle {\frac {1}{\cos(x)}}}$ .

A graph of ${\displaystyle \cot(x)}$ . ${\displaystyle \cot(x)}$ is defined as ${\displaystyle {\frac {1}{\tan(x)}}}$ or ${\displaystyle {\frac {\cos(x)}{\sin(x)}}}$ .

Note that ${\displaystyle \tan(x)}$ , ${\displaystyle \sec(x)}$ , and ${\displaystyle \csc(x)}$ are unbounded, positive or negative. While ${\displaystyle \tan(x)}$ (and ${\displaystyle \cot(x)}$) can take any value, ${\displaystyle \sec(x)}$ and ${\displaystyle \csc(x)}$ can never lie between -1 and 1.