Question

How do you find the amplitude and period of `y=2 cos(x+(pi/3))`?

Answer 1

`2,2pi`

Explanation:

`"the standard form of the cosine is"`

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

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

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

`"here "a=2,b=1,c=pi/3" and "d=0`

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