1. The problem asks to compare the amplitudes of the functions $f(x) = -1.8 \cos x$ and $g(x) = -3.6 \cos x$. 2. Recall that the amplitude of a cosine function $a \cos x$ is the absolute value of the coefficient $a$. 3. For $f(x)$, the amplitude is $|{-1.8}| = 1.8$. 4. For $g(x)$, the amplitude is $|{-3.6}| = 3.6$. 5. To compare, divide the amplitude of $g(x)$ by the amplitude of $f(x)$: $$\frac{3.6}{1.8} = 2$$ 6. This means the amplitude of $g(x)$ is two times the amplitude of $f(x)$. Final answer: The amplitude of $g(x)$ is two times the amplitude of $f(x)$.