# How do you find the amplitude and period of y=1/2cos(3/4theta)?

Feb 10, 2017

$\text{amplitude "=1/2," period } = \frac{8 \pi}{3}$

#### Explanation:

The standard form of the $\textcolor{b l u e}{\text{cosine function}}$ is.

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

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

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

$\text{here } a = \frac{1}{2} , b = \frac{3}{4} , c = 0 , d = 0$

$\Rightarrow \text{amplitude "=|1/2|=1/2" and period } = \frac{2 \pi}{\frac{3}{4}} = \frac{8 \pi}{3}$