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