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

Solution Steps

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

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.

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

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

Final Answer