Question

How do you determine the amplitude, period and vertical translation of `y=3sin4x-5`?

Answer 1

`3,pi/2,-5`

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=4,c=0,d=-5`

`"amplitude "=|3|=3," period "=(2pi)/4=pi/2`

`"vertical shift "=-5`