question\nwrite the equation of the trigonometric function shown in the graph.\n$y=squarecos(square x)+square$

Explanation:

Step1: Determine the amplitude

The amplitude $A$ of a cosine - function $y = A\cos(Bx)+C$ is half of the vertical distance between the maximum and minimum values. The maximum value of the function is $y = 5$ and the minimum value is $y=- 5$. So, $A=\frac{5 - (-5)}{2}=5$.

Step2: Determine the period and find $B$

The period $T$ of a cosine - function $y = A\cos(Bx)+C$ is given by $T=\frac{2\pi}{B}$. The graph repeats itself over an interval of $2\pi$. So, $T = 2\pi$. Since $T=\frac{2\pi}{B}$ and $T = 2\pi$, then $B = 1$.

Step3: Determine the vertical shift

The vertical shift $C$ is the mid - value between the maximum and minimum values. The mid - value between $y = 5$ and $y=-5$ is $\frac{5+( - 5)}{2}=0$.

Answer:

$y = 5\cos(x)+0$