IXL - Write equations of sine and cosine functions using properties (Algebra 2 practice)

Find an equation for a sinusoidal function that has period

amplitude 1, and contains the point

(

–

)

Write your answer in the form

(

)

cos

(

)

where

and

are real numbers.

(

)

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Learn with an example

question

Find an equation for a sinusoidal function that has period

amplitude 1, and contains the point

–

Write your answer in the form

(

)

sin

(

)

where

and

are real numbers.

(

)

key idea

A sinusoidal function has one of two forms:

A
sin
(
B
x
+
C
)
+
D
A
cos
(
B
x
+
C
)
+
D

where

is the amplitude and

is the

period.

solution

Use the amplitude and period to find the numbers

and

in the equation

(

)

sin

(

)

Begin with the amplitude.

amplitude

This means

±1

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

Finally, use

–

to find

and

(

)

sin

(

)

–

sin

–

There are many choices for

and

that will satisfy this equation. For simplicity, choose

and solve for

–

sin

–

An equation for this function is:

(

)

sin

(

)

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Not feeling ready yet? These can help:

KK.3Write equations of sine functions using properties

KK.8Write equations of cosine functions using properties

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