write the equation of the trigonometric function shown in the graph.\ny=squarecos(square x)+square

Explanation:

Step1: Determine the amplitude

The amplitude $A$ of a cosine - function $y = A\cos(Bx)+C$ is half the distance between the maximum and minimum values. The maximum value of the function in the graph is $y = 1$ and the minimum is $y=-1$. So, $A=\frac{1 - (-1)}{2}=1$.

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 every $2\pi$. So, $T = 2\pi$. Since $T=\frac{2\pi}{|B|}$ and $T = 2\pi$, then $|B| = 1$. The standard form of the cosine function is used here, so $B = 1$.

Step3: Determine the vertical shift

The vertical shift $C$ of a cosine - function $y = A\cos(Bx)+C$ is the mid - value between the maximum and minimum values. The mid - value between $y = 1$ and $y=-1$ is $C = 0$.

Answer:

$y = 1\cos(1x)+0$ or simply $y=\cos(x)$