write the equation of the trigonometric function shown in the graph. try whole numbers or unit fractions for…

Explanation:

Step1: Determine the amplitude

The amplitude $A$ of a sine - function $y = A\sin(Bx)+C$ is half of the vertical distance between the maximum and minimum values. The maximum value of the function in the graph is $y = 5$ and the minimum value is $y=- 5$. So, $A=\frac{5 - (-5)}{2}=5$.

Step2: Determine the period and find $B$

The period $T$ of a sine - function $y = A\sin(Bx)+C$ is given by $T=\frac{2\pi}{B}$. Looking at the graph, we can see that the period $T = 15$. So, $15=\frac{2\pi}{B}$, and solving for $B$ gives $B=\frac{2\pi}{15}$.

Step3: Determine the vertical shift

The mid - line of the sine function is the average of the maximum and minimum values. The mid - line is $y=\frac{5+( - 5)}{2}=0$, so the vertical shift $C = 0$.

Answer:

$y = 5\sin\left(\frac{2\pi}{15}x\right)+0$