Trigonometric functions

Remarks

Here $Z_{\cos} = \set{\pi/2 + k\pi : k \in \Z}$ and $Z_{\sin} = \set{k\pi : k \in \Z}$.

Example: $x = \pi/3$ lies in neither set, and $\sin(\pi/3) = \sqrt3/2$, $\cos(\pi/3) = 1/2$, so $\tan(\pi/3) = \sqrt3$, $\sec(\pi/3) = 2$, $\cot(\pi/3) = 1/\sqrt3$ and $\csc(\pi/3) = 2/\sqrt3$.

Non-example of a value: $\tan(\pi/2)$ is not defined, because $\cos(\pi/2) = 0$, so $\pi/2 \in Z_{\cos}$; the tangent tends to $+\infty$ as $x \to \pi/2$ from the left.

The functions $\sin$, $\cos$, $\sec$ and $\csc$ have period $2\pi$, and $\tan$ and $\cot$ have period $\pi$. The tangent function has its own node.