# How do you find the amplitude, period, and shift for y= 4/3 cos (x/2)?

Mar 4, 2018

$A m p l i t u \mathrm{de} = a = \left(\frac{4}{3}\right)$

$P e r i o d$= (2pi) / |b| = 4pi

Phase shift $= \frac{c}{b} = 0 \textcolor{w h i t e}{a a a}$ $\textcolor{red}{0}$ to the right

#### Explanation:

Standard form of equation for cosine function is

$y = a \cos \left(b x - c\right) + d$

$y = \left(\frac{4}{3}\right) \cos \left(\frac{x}{2}\right)$

$A m p l i t u \mathrm{de} = a = \left(\frac{4}{3}\right)$

$P e r i o d$= (2pi) / |b| = (2pi) / (1/2) = 4pi

Phase shift $= \frac{c}{b} = 0 \textcolor{w h i t e}{a a a}$ $\textcolor{red}{0}$ to the right

graph{(4/3) cos (x/2) [-10, 10, -5, 5]}