Question

How do you find the amplitude, period, phase shift for `y=sin(x-pi/4)`?

Answer 1

`1,2pi,pi/4`

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

Here a = 1 , b = 1 , c `=-pi/4` and d = 0

`rArr"amplitude "=|1|=1," period "=(2pi)/1=2pi`

`"and phase shift "=-(-pi/4)/1=pi/4`