Identify the period in terms of π and the amplitude for the sinusoid y = -3 + 2cos(4x - 20).

To determine the period and amplitude of the sinusoid given by the equation ( y = -3 + 2\cos(4x - 20) ), we can analyze its components.

In the general form of a cosine function, ( y = A + B\cos(Cx - D) ):

• ( A ) is the vertical shift,

• ( B ) is the amplitude,

• ( C ) affects the period.

1. Amplitude: The amplitude is given by the coefficient of the cosine function, which is ( B ). In this case, ( B = 2 ). Therefore, the amplitude of this sinusoidal function is 2. This indicates how far the function varies from its central axis, which is the vertical shift defined by ( A = -3 ).

2. Period: The period of the cosine function is calculated using the formula ( P = \frac{2\pi}{|C|} ). Here, ( C = 4 ), so the period becomes:

[

P = \frac{2\pi}{|4|} = \frac{2\pi}{4} = \frac{\pi}{2}.

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