## Friday, May 20, 2011

### Cosecant Function

Cosecant function is a reciprocal of sine function. If $f(x)=\sin x$, then $g(x)=\frac{1}{\sin x}=\csc x$. Generally, cosecant function can be written as $f(x) = a \csc (bx+c) +d$.

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

You may change the values of a = 1, b = 1, c = 0 and d = 0 and think about the construction of csc(x) from sin(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 $f(x) = a \csc (bx+c)+d$. What can you say about the effects of these values towards the function csc (x)?

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