Question

How do you identify the amplitude, period and phase shift given the function `y=3sin(2x-pi/2)`?

Answer 1

`3,pi,pi/4`

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=2,c=-pi/2" and "d=0`

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

`"phase shift "=-(-pi/2)/2=pi/4`