# How do you graph and list the amplitude, period, phase shift for y=1/2cosx+5/2?

Sep 22, 2016

Amplitude $\frac{1}{2}$, period$= 2 \pi$ and phase shift$= 0$ (none).

#### Explanation:

The general equation of cosine is $y = A \cos \left(B x - C\right) + D$ where

$A =$ amplitude
$\frac{2 \pi}{\left\mid B \right\mid} =$ period
$\frac{C}{B} =$ phase shift
$D =$ vertical shift

For the equation $y = \frac{1}{2} \cos x + \frac{5}{2}$
$A = \frac{1}{2}$, $B = 1$, $C = 0$, $D = \frac{5}{2}$
Amplitude = $\frac{1}{2}$
Period=$\frac{2 \pi}{\left\mid 1 \right\mid} = 2 \pi$ (the "regular" period of cosine)
Phase shift = $\frac{0}{1} = 0$ (no phase shift)
Vertical shift =$\frac{5}{2}$ (up $\frac{5}{2}$)