IXL - Write equations of sine and cosine functions from graphs (Algebra 2 practice)

Find an equation for the cosine graph,

(

)

Write your answer in the form

(

)

cos

(

)

where

and

are real numbers.

(

)

ref_doc_title.

Learn with an example

question

Find an equation for the cosine graph,

(

)

Write your answer in the form

(

)

cos

(

)

where

and

are real numbers.

(

)

key idea

This is the graph of

cos

(

)

The graph of

cos

(

)

is similar to the graph of

cos

(

)

The numbers

and

determine the characteristics of the graph.

absolute value bar
A
absolute value bar
is the
amplitude.
It is half the vertical distance from the graph's maximum to its minimum.
2
pi
absolute value bar
B
absolute value bar
is the
period.
It is the horizontal distance between two consecutive maxima.
y
=
D
is the
midline.
It is a horizontal line that cuts the graph in half.
D
is the vertical
shift.
Its absolute value,
absolute value bar
D
absolute value bar
,
is the vertical distance between the midline and the
x
-axis.
If the
x
-axis
is the midline, then
D
=
0
.

solution

Find the amplitude.

Look at the graph to find the vertical distance from the graph's maximum to its minimum.

Divide the vertical distance by 2 to find the amplitude.

amplitude

Find the period.

Find the horizontal distance between two consecutive maxima.

This distance is

so the period is

Find the vertical shift.

The midline of the graph is the

-axis.

So, the vertical shift is 0.

Find an equation for the graph.

Use the amplitude and period to find the numbers

and

in the equation

(

)

cos

(

)

Begin with the amplitude.

amplitude

This means

±2

Either choice for

will result in a valid equation. Choose

Next, look at the period.

period

This means

±1

Again, either choice for

is valid. Choose

Next, look at the vertical shift.

vertical shift

To summarize,

and

Now find a value of

so that the function

(

)

cos

(

)

fits the graph. Start by locating a point on the graph.

Plug this point into the function and solve for

cos

One value of

that makes this equation true is

So, an equation for the given function is:

(

)

cos

(

)

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Not feeling ready yet? These can help:

KK.2Write equations of sine functions from graphs

KK.7Write equations of cosine functions from graphs

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