Explanation:
The general forms of a wave is:
y = ±A sin(2π/B x) + C
y = ±A cos(2π/B x) + C
where A is the amplitude, B is the period, and C is the centerline.
First graph is a positive sine wave. It has a maximum of 5 and a minimum of -1, so the centerline is at C = (5 + -1) / 2 = 2, and the amplitude is A = (5 − -1) / 2 = 3. The distance between the peaks is B = 8 units.
Therefore:
y = 3 sin(2π/8 x) + 2
y = 3 sin(π/4 x) + 2
The second graph is a negative cosine wave. The maximum is at 5 and the minimum is at 0, so the centerline is at C = (5 + 0) / 2 = 2.5, and the amplitude is A = (5 − 0) / 2 = 2.5. The distance between the peaks is B = 2.
Therefore:
y = -2.5 cos(2π/2 x) + 2.5
y = -2.5 cos(π x) + 2.5