Question

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

Answer 1

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

Explanation:

This graph is a periodic cosine wave.

Amplitude = `(max y - min y)/2 = (2-(-2))/2`,

Period = 2 and

Phase: `4pi`,

comparing with the form

`y = (amplitude) cos( (2pi)/(period)x+phase)`.

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