Question

Can you please help me guys

Answer 1

Answer:

y = ±3 cos(2x+2)+2

Step-by-step 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 :

$\frac{2\pi }{b}=\pi$

b = 2

As phase shift:

$\frac{b}{c}=1$

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.

$\frac{2\pi}{b}= \pi$

is the period.

This implies that

$b=2$

$\frac{b}{c} = 1$

is the phase shift.

This implies that;

$c = 2$

$d = 2$

is the vertical shift.

The possible equations are:

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