GRAPHING COSINE

FIRST WE HAVE TO FACTORIZE

• 5cos(2X+Π/6)-4
• 5cos2(X+Π/3)-4
• Note: notice that if you do distributive property you get the same result indside the original problem
• Now we can carry on with the problem

THE GRAPH

First we will get the period,
The formula for it is 2Π/b.
But what is "b"?
"B" is the number next to the "x".
If we look at the problem we can see that "b" is 2.
5COS(2X+Π/6)-4
2Π/2=Π

Next we have the space between reference points.
The formula for this is period/4.
If we put it all together he have Π/4, we can't simplify it so we'll leave it like that.

Amplitude is very simple. We just have to look at the problem.
5cos2(X+Π/3)-4
Amplitude in this case would be the number before the cosine function.
The amplitude is 5.

Now all we need are the coordinates where we start.
Horizontal and vertical shift.

TO GET THEM, WE HAVE TO LOOK AT THE PROBLEM

• 5cos2(X+Π/3)-4
• The horizontal shift is the number adding or subtracting with the "x"
• In this case Π/3 to the left becuase you do the opposite as it says
• Next you need the vertical
• The vertical shift is the number outside the parentheses in this case 4 down

To have an organized graph you can state your x and y axis.
In our graph we could use the y-axis by 1 digit.
The x-axis could be Π/12, because it's a common denominator of the space between points and the horizontal shift.

GRAPHING

TO START YOU YOU HAVE TO

• Begin at (0,0) then move to your horizontal and vertical shift
• When you have your point, apply your amplitude up
• Then you move what your space between points states Π/4
• Moving up and down your y axis by the amplitude 5 down
• At the end you want to form a "u" so you start going down then rising

YOUR FINAL RESULT