Question

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

Answer 1

Answer:

$\frac{\pi }{4}$

Step-by-step explanation:

The standard form of the cosine function is

y = a cos(bx + c)

where a is the amplitude, period = $\frac{2\pi }{b}$ and

phase shift = - $\frac{c}{b}$

here b = 3 and c = - $\frac{3\pi }{4}$, hence

phase shift = - $\frac{-\frac{3\pi }{4} }{3}$ = $\frac{\pi }{4}$

Answer 2

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

.

Tap for more steps...

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 ;-;