## Friday, May 20, 2011

### Cotangent Function

Cotangent function is a reciprocal for tangent function. If $f(x)=\tan x$, then $g(x)=\frac{1}{\tan x}=\cot x$. Generally, cotangent function can be written as $f(x) = a \cot (bx+c) +d$.

Now, consider only $f(x) = \cot x=\frac{1}{\tan x}$,
as tan(x) approaches to 0, cot(x) approaches ∞ or -∞,
as tan(x) approaches ∞ or -∞, cot(x) approaches 0.

You may change the values of a = 1, b = 1, c = 0 and d = 0 and think about the construction of cot(x) from tan(x). After that, you may alter the values to look at the shifting, scaling or reflecting of the graphs.

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Slide the values of a, b, c and d to observe the changes of the graph $f(x) = a \cot (bx+c) +d$. What can you say about the effects of these values towards the function cot (x)?

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