# What is the amplitude, period and the phase shift of y = 2 cos (pi x + 4pi) ?

Jan 6, 2017

Amplitude: 2. Period : 2 and phase $4 \pi$=12.57 radian, nearly.

#### Explanation:

This graph is a periodic cosine wave.

Amplitude = $\frac{\max y - \min y}{2} = \frac{2 - \left(- 2\right)}{2}$,

Period = 2 and

Phase: $4 \pi$,

comparing with the form

$y = \left(a m p l i t u \mathrm{de}\right) \cos \left(\frac{2 \pi}{p e r i o d} x + p h a s e\right)$.

graph{2 cos (3.14x+12.57) [-5, 5, -2.5, 2.5]}