>> This is your Math Gal,
Julie Harland.
Please visit my web site
at yourmathgal.com where all
of my videos are organized
by topic.
All right.
Here's our second video
on graphing a
cotangent function.
So let's do this one.
Y equals 2, the cotangent
of 2 X. All right,
so first let's figure
out the period.
So remember the period
for the cotangent is Pi.
So you have to do Pi divided
by B. And in this case,
B is the coefficient of X,
it's always Pi over 2.
So the period
for the cotangent is Pi
over 2.
So that means
when we're graphing it,
we're going
to get a full period
between zero and Pi over 2.
Okay, there we are.
And then the cotangent
function, remember also
where the asymptotes are,
the cotangent
of zero is undefined,
and at the end of the period
which is also Pi over 2,
it is also undefined.
So if I want,
I could go over here
where Pi is,
there would be another place.
Now in between here there's
some points, right?
And that's
where the zeros are.
There's a zero in the middle.
So the last thing to do,
let's use our guidelines here.
So let's market on the X axis,
let's say that's 1
and that's 2.
Oops. Trying
to get away from me.
Okay, so of course just keep
in mind you could always plug
in a bunch of Y --
a bunch of X's
and compute this, right?
Okay, it's better to remember
that the cotangent function
goes down, okay?
And normally it goes
in between the 0 and --
in between the Y axis
and the 0 point is usually
up here at 1.
But because it's got
to 2 times it, it's going be
up here at 2.
So that's going to be a guide.
And then in between 0
and the next asymptote,
usually it's
down at negative 1.
It's going to go
down to negative 2 because of
that coefficient.
And those are our guidelines.
And there we go.
I'm not graphing
this perfectly.
You might want
to get a graphing calculator
and see what it looks a little
better -- depends
on how you draw your X
and Y axis
and how you label it,
looks prettier,
depending on how you do it.
Looks more like that, usually.
So I could also have a graph
to go over here,
I'm going to have a point
over here,
I'm going to have a point
down here.
And just try
to make it look a little
curvy, as best you can.
I know it's not easy.
And there we've got the graph
of Y equals the cotangent
of 2 X. All right,
so what do we have here?
We've got the period is Pi
over 2.
Let's state what our
asymptotes are.
We have vertical asymptotes,
right?
They're lines.
X equals. All right,
where does it go through?
Well, the first one is just 0,
that's easy.
And then we're going to add
on the period
to get the next one.
So it's just Pi over 2.
So the cool thing is
for the cotangent,
it's whatever the period is
times K. So it's Pi
over 2 times K,
or Pi K over 2.
K is an element.
That's always going to be true
if there are no --
if there's no phase shift.
If there's no phase shift the
vertical asymptotes basically
are going to do X equals --
you're going to put
in the period.
Put period in here.
Period times K.
And K is an element
of the integer.
So that make might it easier
for the cotangent.
This is your math gal Julie
hare land.
Please visit my web site
at yourmathgal.com where all
of my videos are organized
by topic.