# How do you graph y=secpix?

Oct 24, 2016

$\sec \left(\pi x\right) = \frac{1}{\cos} \left(\pi x\right)$

#### Explanation:

To graph any inverse function like this it is often easier to graph the normal function lightly and then draw the inverse over the top.

so for this graph $\cos \left(\pi \cdot x\right)$

which goes through the y-axis at (0,1) has min at (1,-1) and max at (2,1)

with a period of 2. giving you a graph like this,

graph{cos(pix) [-2, 2, -4, 4]}

now let's look at some of the features of the graph and decide what will happen when we do $\frac{1}{f} \left(x\right)$.

1. any points where y=1 or y=-1 will remain the same
2. any points whey y=0 will become an asymptote
3. points at $y = \frac{1}{2}$ will go to$y = 2$, points at $y = 2$ will go to $y = \frac{1}{2}$ ect.

now we can do a rough sketch of what the graph will look like.

graph{1/(cos(pix)) [-2, 2, -4, 4]}

It is easier to see the relationship if you superimpose them on one another