Question

Can you please help me guys

Answer 1

y = ±3 cos(2x+2)+2

Explanation:

We have to find the cosine function.

GIVEN:

amplitude=3

period= π

phase shift = 1

vertical shift = 2

The general form of cosine function is:

y = acos (bx+c) +d

Where a is the amplitude, which is equal to IaI = 3

a= ±3

As period is :

`(2\pi )/(b)=\pi`

b = 2

As phase shift:

`(b)/(c)=1`

c=2

Vertical shift d= 2.

Put the value of a,b,c,d in the general equation:

y = a cos (bx+c) +d

y = ±3 cos(2x+2)+2 is the required equation.

Answer 2

ANSWER


`y = 3 \cos(2x + 2) + 2`

or

`y= -3\cos(2x + 2) + 2`

Any of these two are correct

EXPLANATION

The general cosine function is


`y = a \cos(bx + c) + d`

where


`|a|=3`


`a=\pm3`

is the amplitude.


`(2\pi)/(b)= \pi`

is the period.

This implies that


`b=2`


`(b)/(c) = 1`

is the phase shift.

This implies that;


`c = 2`


`d = 2`

is the vertical shift.

The possible equations are:


`y = \pm \: 3 \cos(2x \pm2)+2`