Question

What is the phase shift of y = cos(3x - 3pi/4 )?

Answer 1

Use the form

a

cos

(

b

x

−

c

)

+

d

acos(bx-c)+d

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

a

=

4

a=4

b

=

3

b=3

c

=

π

4

c=π4

d

=

0

d=0

Find the amplitude

|

a

|

|a|

.

Amplitude:

4

4

Find the period using the formula

2

π

|

b

|

2π|b|

.

Tap for more steps...

Period:

2

π

3

2π3

Find the phase shift using the formula

c

b

cb

.

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Phase Shift:

π

12

π12

Find the vertical shift

d

d

.

Vertical Shift:

0

0

List the properties of the trigonometric function.

Amplitude:

4

4

Period:

2

π

3

2π3

Phase Shift:

π

12

π12

(

π

12

π12

to the right)

Vertical Shift:

0

0

i think ;-;

Answer 2

`(\pi )/(4)`

Explanation:

The standard form of the cosine function is

y = a cos(bx + c)

where a is the amplitude, period =
`(2\pi )/(b)` and

phase shift = -
`(c)/(b)`

here b = 3 and c = -
`(3\pi )/(4)`, hence

phase shift = -
`(-(3\pi )/(4) )/(3)` =
`(\pi )/(4)`