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

May 19, 2017

Amplitude: $\frac{1}{2}$

Period: $8 \pi$

#### Explanation:

The amplitude is the value multiplied by the cosine.

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

$\frac{2 \pi}{\frac{2}{8}} = 8 \pi$

May 20, 2017

$\frac{1}{2} , 8 \pi$

#### Explanation:

$\text{the standard form of the "color(blue)"cosine function}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a \cos \left(b x + c\right) + d} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where amplitude "=|a|," period } = \frac{2 \pi}{b}$

$\text{phase shift "=-c/b," vertical shift } = d$

$\text{here } a = \frac{1}{2} , b = \frac{1}{4} , c = d = 0$

$\Rightarrow \text{ amplitude "=|1/2|=1/2," period} = \frac{2 \pi}{\frac{1}{4}} = 8 \pi$