what is the cosine equation of the function shown? enter your answer by filling in the boxes. enter any…

Explanation:

Step1: Determine the amplitude

The amplitude $A$ of a cosine - function $y = A\cos(Bx - C)+D$ is half the distance between the maximum and minimum values of the function. From the graph, the maximum value is $y = 4$ and the minimum value is $y=-4$. So, $A=\frac{4 - (-4)}{2}=4$.

Step2: Determine the period and the value of $B$

The standard period of the cosine function $y = \cos(x)$ is $2\pi$. For the function $y=\cos(Bx)$, the period $T=\frac{2\pi}{B}$. From the graph, the period $T = 4\pi$. So, $\frac{2\pi}{B}=4\pi$. Solving for $B$, we get $B=\frac{1}{2}$.

Step3: Determine the phase - shift and vertical - shift

The graph of $y = \cos(x)$ has a maximum at $x = 0$. The given cosine - function has a maximum at $x = 0$, so the phase - shift $C = 0$. Also, the mid - line of the function is $y = 0$, so the vertical - shift $D = 0$.

Answer:

$f(x)=4\cos(\frac{1}{2}x)+0$ or simply $f(x)=4\cos(\frac{1}{2}x)$