Question

How do you find the amplitude, period, phase shift for `y=1/2 cosx`?

Answer 1

`1/2,2pi,0`

Explanation:

`"the standard form of the 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=1/2,b=1,c=d=0`

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

`"there is no phase shift"`