# Finding the domain and the range of $\cot x$

I need to find the domain and the range of this function:

$$h(T) = \cot T$$

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What is cot? Cotangent? Is this homework? Why don't you look for any book/internet reference on elementary trigonometry? –  Siminore Jul 4 '12 at 8:07
–  Gigili Jul 4 '12 at 8:18

Domain: $\mathbb R-{k\pi} ,k \in \mathbb Z$
Range : $\mathbb R$
if $f(x)=cot(x)$ is $\frac{\cos(x)}{\sin(x)}$ , domain of a function is set of the points where $f(x)$ is defined. In a fraction, the denominator can't be zero. So:
$\sin(x) \neq 0 \implies x \neq k\pi ,k \in Z= \{\dots,-2,-1,0,1,2,\dots\}$
Range of a function is set of the points $f(x)$ can generate.
In this case, $\cot(x)$ can generate all the numbers in $\mathbb R$ (real numbers).
Please use $\LaTeX$. –  Gigili Jul 4 '12 at 8:25