# What is the amplitude and period of y=-4cos2x?

Jan 13, 2018

$4 , \pi$

#### Explanation:

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

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

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

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

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

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