write the equation of the trigonometric function shown in the graph.\n$y=squaresin(square x)+square$

Explanation:

Step1: Determine the amplitude

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

Step2: Determine the period and find $B$

The period $T$ of a sine - function $y = A\sin(Bx)+C$ 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 $B = 1$.

Step3: Determine the vertical shift

The mid - line of the function is $y = 0$. For a sine - function $y=A\sin(Bx)+C$, the vertical shift is $C$. Since the mid - line is $y = 0$, then $C = 0$.

Answer:

$y = 2\sin(x)+0$ or simply $y = 2\sin(x)$