## Friday, May 20, 2011

### Secant Function

Secant function is a reciprocal for cosine function. If $f(x) = \cos x$, then $g(x)=\frac{1}{\cos x}=\sec x$. Generally, secant function can be written as $f(x) = a \sec (bx+c) +d$.

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

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

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