# How do you find the amplitude and period of y=6sin(1/8x)?

Aug 27, 2016

amplitude = 6, period $= 16 \pi$

#### Explanation:

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

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

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

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

here a = 6 , $b = \frac{1}{8}$ , c = 0 and d = 0

$\Rightarrow \text{amplitude" =|6|=6" and period} = \frac{2 \pi}{\frac{1}{8}} = 16 \pi$