200k views
3 votes
Find an equation of the cosine function whose graph is shown below.

f(x)=____cos_____x+______

Find an equation of the cosine function whose graph is shown below. f(x)=____cos_____x-example-1
User Dotty
by
7.7k points

2 Answers

3 votes

Answer:


y=3\text{cos}(2x)+1

Explanation:

We have been given an image of trigonometric function. We are asked to find the equation of the given function.

We know that standard form of a cosine function is
y=A\cdot \text{cos}(Bx-C)+d, where,

A = Amplitude of function


(2\pi)/(B) = Period of function,

C = Horizontal shift or phase shift,

D = Vertical shift.

Upon looking at our given function we can see that amplitude of our given function is 3 as average of maximum and minimum of our given function is
(4--2)/(2)=(4+2)/(2)=(6)/(2)=3.

We know that mid-line of our given function is
y=1, therefore, our function is shifted upwards by 1 unit.

We can see that period of our given function is
\pi.

Let us find the value of B using formula:


\pi=(2\pi)/(B)


B=(2\pi)/(\pi)


B=2

Therefore, our required equation is
y=3\text{cos}(2x)+1.

User Jeremyharris
by
8.2k points
5 votes
Short Answer: y = 3*cos(2x) + 1
Remark
This is not part of the answer, but it will help you to see what is going on. Begin by shifting the cos graph 1 unit down. That will that the cos has a minimum of -3 and a max of + 3

What that tells you is the part of the equation is
y = 3*cos(x)

Step One
Show that the graph is of something that resembles y = 3*cos(x)
the test way to check this is to put in 0 for x
3*cos(0) = 3*1 = 3. But why is it 4 and -2 instead of 3 and -3.

Step Two
Show how the graph is shifted up one space.
y movement is always recorded behind how the variable is determined.
So if the graph is shifting up one, you should do this.
y = 3cos(x) + 1

Step Three
The graph seems to be starting over at n*pi rather than n*2pi. How do we adjust for that?
There are 2 choices. Either there is a 4 in front of the x or there is a 1/2 in front of the x. Before just telling you, consider the graph below.
Violet is 3*cos(1/2 x)
Blue is 3*cos (x)
orange is 3*cos(2*x)

You want the graph that starts over again at x = 3.14 rather than at x = 6.28
The one that starts over at y = 3*cos(2x)
The rule is that if you want to compress a trigonometric function, use a constant such that a > 1 y = 3*cos(a*x). It is the a I'm trying to explain.

Step 4
Is there a phase shift?
No. If there was cos(x) would not have a maximum at x = 0

Answer y = 3*cos(2x) + 1
Find an equation of the cosine function whose graph is shown below. f(x)=____cos_____x-example-1
User Takoyaro
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories