>> This is Your Math Gal,
Julie Harland.
Please visit my Web site
at YourMathGal.com,
where all of my videos are
organized by topic.
This is Part 3
of Graphing Cosine Functions.
On this video we are going
to graph y equals the cosine
of x plus 2.
OK, as a reminder,
here's the graph
of y equals cosine of x.
So here are some -
the five key ordered pairs.
And I have a couple
of cycles here,
but we have one cycle going
in between zero and 2 pi here.
Here we have got the domain,
the range, the amplitude,
and the period.
So remember,
if you go from zero to 2 pi
for the cosine,
the y coordinates go 1, zero,
negative 1, zero, 1.
So how would we graph y equals
the cosine of x plus 2?
We if you remember those
values for the cosine of x
that I just showed you,
remember the values,
when it's zero the cosine
of x - the cosine
of zero would be 1, zero,
negative 1, zero, 1.
Right? But what are we doing?
We are adding 2 to each
of those values.
[ Writing on board ]
So the y coordinates will be
3, 2, 1, 2, 3.
So how does that look
over here?
We have got the ordered
pair (0,3).
Oops. I don't know why this
does it on me.
All right,
so we have got (0,3),
(pi over 2,2), (pi,1),
(3 pi over 2,2).
Whoops.
[ Pause ]
And then we have got (2 pi,3).
And that gives us one
complete cycle.
Now make sure you don't think
of that as a V. Remember this
is curved.
We could keep going here
and do some more ordered pairs
if we want,
and where it starts repeating.
And then we just make a nice
little sketch.
So make sure you are sketching
it with curves like I am.
And there we have the graph
of y equals the cosine
of x plus 2.
So the domain:
What values can you put
in for x?
Anything. It's always
between negative infinity
and infinity for the cosine.
Now the range:
Where do the y values
go between?
Well the lowest value is 1,
and the highest value is 3.
You can see
that from the graph,
or you could look over here
in the chart.
So it's between 1 and 3.
The amplitude is half
the height.
So for instance,
if the range is 1 and 3,
that's a height of 2;
half of that is 1.
Or remember,
it's just the absolute value
of the coefficient of cosine
of x. So it's going to be 1.
And the period is 2 pi.
Now you might notice this
looks, again,
just like y equals cosine
of x except all - it's picked
up two spaces up.
All the values
that were y are two higher
than they were
for y equals cosine of x.
So remember for the cosine
of x, we had (0,1);
here we have (0,3).
So if you were
to graph y equals cosine
of x here,
it would just be below it two
spaces below this one.
This is Your Math Gal,
Julie Harland.
Please visit my Web site
at YourMathGal.com,
where all of my videos are
organized by topic. ------------------------------e74212391922--