Questions: Determine the amplitude of the following trigonometric function. f(x)=-4-5 cos (2 x-π)

Determine the amplitude of the following trigonometric function. f(x)=-4-5 cos (2 x-π)
Transcript text: Review Passage Determine the amplitude of the following trigonometric function. $f(x)=-4-5 \cos (2 x-\pi)$
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Solution

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Solution Steps

Step 1: Identify the Function

The given trigonometric function is \[ f(x) = -4 - 5 \cos(2x - \pi). \]

Step 2: Determine the Amplitude

In the general form of a cosine function, \( f(x) = A \cos(Bx - C) + D \), the amplitude is represented by the absolute value of the coefficient \( A \) in front of the cosine term.

Step 3: Extract the Coefficient

From the function, we identify the coefficient of the cosine term: \[ A = -5. \]

Step 4: Calculate the Amplitude

The amplitude is calculated as the absolute value of \( A \): \[ \text{Amplitude} = |A| = |-5| = 5. \]

Final Answer

\(\boxed{5}\)

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