IXL - Find properties of sine and cosine functions (Precalculus practice)

or

Find the period of the sinusoidal function.

Simplify any fractions.

period

=

ref_doc_title.

or

Learn with an example

question

Find the vertical shift of the sinusoidal function.

Simplify any fractions.

vertical shift

=

key idea

A sinusoidal function has one of two forms:

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

This is the graph of

cos

(

x

)

:

The graph of

A

cos

(

B

x

+

C

)

+

D

is similar to the graph of

cos

(

x

)

.

The numbers

A

,

B

,

C

,

and

D

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.
absolute value bar
B
absolute value bar
2
pi
is the
frequency.
It is the reciprocal of the period.
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

The midline of the graph is the

x

-axis.

So, the vertical shift is 0.

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