Tanc function

This article is about a particular function from a subset of the real numbers to the real numbers. Information about the function, including its domain, range, and key data relating to graphing, differentiation, and integration, is presented in the article.
View a complete list of particular functions on this wiki

For functions involving angles (trigonometric functions, inverse trigonometric functions, etc.) we follow the convention that all angles are measured in radians. Thus, for instance, the angle of $90\,^{\circ }$ is measured as $\pi /2$.

Definition

The function is defined at all real numbers except odd multiples of $\pi /2$, and the definition is as follows:

$\operatorname {tanc} \,x:=\left\lbrace {\begin{array}{rl}1,&x=0\\,{\frac {\tan x}{x}},&x\neq 0,x\neq n\pi +\pi /2,n\in \mathbb {Z} \end{array}}\right.$

Thus, it is the function obtained by filling in removable discontinuities in the pointwise quotient of the tangent function by the identity function.

Alternatively, it can be defined as the pointwise quotient of the sinc function by the cosine function.