The amplitude, period, and phase-shift of the function are;
Amplitude = 8
Period = π
Phase shift = 3
The graph of the sinusoidal function, f(x) = 8·cos(2·x - 6), created with MS Excel is attached
The steps used to find the parameters of the function can be presented as follows;
The amplitude of the
The sinusoidal function can be presented as follows;
f(x) = 8·cos(2·x - 6)
The general form of a sinusoidal function is; f(x) = A·trig·(B·x - C) + D, where;
Trig represents a sine or cosine function
A = The amplitude
B = The period or speed function
Period = 2·π/B
C/B = The horizontal phase shift
D = The vertical shift
Comparing the specified function, we get;
A = 8, B = 2, C/B = 6/2
Therefore;
The amplitude, A = 8
The period is; 2·π/2 = π
The horizontal phase shift is; 6/2 = 3
Please find attached the graph of the function over a period, π, showing the maxima, minima, and zeros, created with MS Excel