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

Explanation:

Step1: Determine the amplitude

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

Step2: Determine the period and find $B$

The period $T$ of the sine - function is the distance between two consecutive peaks or troughs. Here, $T = 2\pi$. The formula for the period of $y=\sin(Bx)$ is $T=\frac{2\pi}{B}$. Since $T = 2\pi$, then $B = 1$.

Step3: Determine the vertical shift

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

Answer:

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