Question

How do you write an equation of the sine function with amplitude 5, period 3pi, and phase shift –pi?

Answer 1

`y=5sin(2/3x+(2pi)/3)`

Explanation:

The standard form of the `color(blue)"sine function"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=asin(bx+c)+d)color(white)(2/2)|)))`

`"where amplitude "=|a|, "period "=(2pi)/b`

`"phase shift "=-c/b" and vertical shift "=d`

We have to find a, b and c

`• a=5to"given"`

`• (2pi)/b=3pirArrb=(2pi)/(3pi)=2/3`

`• -c/(2/3)=-pi`

`rArr3/2c=pirArrc=(2pi)/3`

`rArry=5sin(2/3b+(2pi)/3)larr" is the equation"`