Question

How do you find period, amplitude, phase shift and midline of `y = 3 + 2cos(x + (pi/4))`?

Answer 1

`"see explanation"`

Explanation:

`"the standard form of the "color(blue)"cosine function"` is.

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

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

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

`"here "a=2,b=1,c=pi/4" and "d=3`

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

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

`"maximum value "=3+2=5`

`"minimum value "=3-2=1`

`rArr"midline "y=1/2(5+1)=3`