write the equation of the trigonometric function shown in the graph. use a positive coefficient on sine for…

Explanation:

Step1: Determine the amplitude

The general form of a sine - function is $y = A\sin(B(x - C))+D$. The amplitude $|A|$ is the distance from the mid - line to the maximum or minimum value of the function. Observing the graph, the mid - line is $y = 0$, and the maximum value is $y = 1$ and the minimum value is $y=-1$, so $A = 1$.

Step2: Determine the period

The period $T$ of a sine function $y=\sin(B(x - C))+D$ is given by $T=\frac{2\pi}{|B|}$. The graph repeats itself over an interval of $2\pi$. For the standard sine function $y = \sin(x)$, the period is $2\pi$, and here the period is also $2\pi$, so $B = 1$.

Step3: Determine the phase - shift

The phase - shift is given by $C$. The standard sine function $y=\sin(x)$ has a zero - crossing at $x = 0$. Looking at the given graph, the zero - crossing that behaves like the standard sine function's starting point is at $x = 0$, so $C = 0$.

Step4: Determine the vertical shift

The vertical shift is given by $D$. Since the mid - line of the function is $y = 0$, $D = 0$.

Answer:

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