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

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 of the function. The maximum value of the given function is $y = 2$ and the minimum value is $y=- 2$. 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 distance between two consecutive peaks (or troughs) of the given function is $2\pi$. 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 $C$ of a sine - function $y=A\sin(Bx)+C$ is the mid - value between the maximum and minimum values. The mid - value between $y = 2$ and $y=-2$ is $C = 0$.

Answer:

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