Question

What is the amplitude, period, phase shift and vertical displacement of `y=sin(x+pi/4)`?

Answer 1

`1,2pi,-pi/4,0`

Explanation:

`"the equation of the sine in standard form is"`

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

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

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

`"here "a=1,b=1,c=pi/4,d=0`

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

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

`"there is no vertical displacement"`