Y =3cos (2x-1) +0,3
amplitude

Y

=

3

cos

(

2

x

-

1

)

Use the form

to

cos

(

b

x

-

c

)

+

d

to find the variables used to find the amplitude, period, phase shift, and vertical shift.

to

=

3

b

=

2

c

=

1

d

=

0

Find the amplitude

|

to

|

.

Amplitude:

3

Find the period using the formula

2

π

|

b

|

.

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Period:

π

Find the phase shift using the formula

c

b

.

Tap for more steps ...

Phase shift:

1

2

Find the vertical displacement

d

.

Vertical displacement:

0

List the properties of trigonometric functions.

Amplitude:

3

Period:

π

Phase shift:

1

2

(

1

2

on the right)

Vertical displacement:

0

Select some points on the graph.

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x

F

(

x

)

1

2

3

π

4

+

1

2

0

π

2

+

1

2

-

3

3

π

4

+

1

2

0

π

+

1

2

3

The trigonometric function can be drawn using the amplitude, period, phase shift, vertical shift, and the points.

Amplitude:

3

Period:

π

Phase shift:

1

2

(

1

2

on the right)

Vertical displacement:

0

x

F

(

x

)

1

2

3

π

4

+

1

2

0

π

2

+

1

2

-

3

3

π

4

+

1

2

0

π

+

1

2

3Y

=

3

cos

(

2

x

-

1

)

Use the form

to

cos

(

b

x

-

c

)

+

d

to find the variables used to find the amplitude, period, phase shift, and vertical shift.

to

=

3

b

=

2

c

=

1

d

=

0

Find the amplitude

|

to

|

.

Amplitude:

3

Find the period using the formula

2

π

|

b

|

.

Tap for more steps ...

Period:

π

Find the phase shift using the formula

c

b

.

Tap for more steps ...

Phase shift:

1

2

Find the vertical displacement

d

.

Vertical displacement:

0

List the properties of trigonometric functions.

Amplitude:

3

Period:

π

Phase shift:

1

2

(

1

2

on the right)

Vertical displacement:

0

Select some points on the graph.

Tap for more steps ...

x

F

(

x

)

1

2

3

π

4

+

1

2

0

π

2

+

1

2

-

3

3

π

4

+

1

2

0

π

+

1

2

3

The trigonometric function can be drawn using the amplitude, period, phase shift, vertical shift, and the points.

Amplitude:

3

Period:

π

Phase shift:

1

2

(

1

2

on the right)

Vertical displacement:

0

x

F

(

x

)

1

2

3

π

4

+

1

2

0

π

2

+

1

+

1

2

0

π

+

1

2

3