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Find the amplitude, period, and phase-shift of the function. Use this information to graph the function over a full period. Label maxima, minima, and zeros of the function.

f(x)= 8 cos (2x-6)

User Arelys
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1 Answer

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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

Find the amplitude, period, and phase-shift of the function. Use this information-example-1
User Jaho
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