Question

How do you find the period and amplitude of `y=1/2cos((2x)/8)`?

Answer 1

Amplitude: `1/2`

Period: `8pi`

Explanation:

The amplitude is the value multiplied by the cosine.

The period can be calculated by dividing `2pi` by the coefficient of the `x` value inside the cosine:

`(2pi) / (2/8) = 8pi`

Answer 2

`1/2,8pi`

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=1/2,b=1/4,c=d=0`

`rArr" amplitude "=|1/2|=1/2," period" =(2pi)/(1/4)=8pi`