# How do you find the amplitude, period and phase shift of  y= -10 cos 2x?

Oct 25, 2016

amplitude = 10 , period$= \pi$

#### Explanation:

The standard form of the cosine function is.

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

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

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

here a = - 10 , b = 2 , c = 0 , d = 0

Hence amplitude = | -10| = 10 and period $= \frac{2 \pi}{2} = \pi$

Since c = d = 0, there is no phase shift or vertical shift.