# How do you find the amplitude and period of y=7/3cos4x?

May 7, 2018

$\text{amplitude "=7/3," period } = \frac{\pi}{2}$

#### Explanation:

$\text{the standard form of the cosine function is}$

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

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

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

$\text{here } a = \frac{7}{3} , b = 4 , c = d = 0$

$\Rightarrow \text{amplitude "=|7/3|=7/3," period } = \frac{2 \pi}{4} = \frac{\pi}{2}$