Question

Can you please help me you guys

Answer 1

`y = 3 \sin( (2)/(3)( x+ (2)/(\pi) )) -`

Or

`y = - 3 \sin( (2)/(3)( x+ (2)/(\pi) )) - 1`

Step-by-step explanation

The general sine function is given by,

`y = a \sin(bx \pm \: c) \pm d`

where

`|a| = 2`

`a =\pm2`

`(2\pi)/(b) = 3\pi`

is the period.

This implies that,

`b = (2)/(3)`

The phase shift is

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

This implies that,

`c = (4)/(3\pi)`

`d = - 1`

is the vertical shift.

The required equation is:

`y = \pm3 \sin( (2)/(3)( x+ (2)/(\pi) )) - 1`