Question

What is the amplitude, period, phase shift and vertical displacement of `y=3sin(3x+pi)-1`?

Answer 1

`3,(2pi)/3,-pi/3,-1`

Explanation:

`"the standard form of the 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`

`"here "a=3,b=3,c=pi" and "d=-1`

`"amplitude "=|3|=3" period "=(2pi)/3`

`"phase shift "=-pi/3" vertical shift "=-1`