Based on the graph shown above, an equation of the sinusoidal function is: A. y = cosx - 1.
In Mathematics and Geometry, the standard form of a cosine function can be represented or modeled by the following mathematical equation (formula):
y = Acos(Bx - C) + D
Where:
- A represents the amplitude.
- B = 2π/P.
- P represents the period.
- C represents the phase shift.
- D represents the center line (midline).
By critically observing the graph shown above, we can logically deduce that this sinusoidal function represents a cosine function because it is symmetrical about the y-axis;
Amplitude, A = 1
Period is 2π, which gives;
B = 2π/2π = 1
Phase (horizontal) shift, C = 0
Midline, d = -1 (since the graph was shifted down 1 unit).
In this context, the graph of the parent function was vertically shifted down by 1 unit in order to produce the transformed cosine function;
f(x) = cosx
y = f(x) - 1
y = cosx - 1