find an equation for the graph shown. type the equation of the given graph in the form y = a sin(ωx) or y =…

Answer:

$y = 5\sin\left(\frac{3\pi}{13}x\right)$

Explanation:

Step1: Determine the amplitude $A$

The maximum value of the graph is $5$ and the minimum is $- 5$. The amplitude $A$ is given by $|A|=\frac{\text{max}-\text{min}}{2}$. So, $A = 5$.

Step2: Determine the period $T$

The graph starts at $x = 0$ and repeats at $x=\frac{26}{3}$. So the period $T=\frac{26}{3}$.

Step3: Find the angular - frequency $\omega$

The formula for the period of a sine or cosine function is $T=\frac{2\pi}{\omega}$. Solving for $\omega$, we get $\omega=\frac{2\pi}{T}$. Substituting $T = \frac{26}{3}$ into the formula, we have $\omega=\frac{2\pi}{\frac{26}{3}}=\frac{3\pi}{13}$.

Step4: Choose the function form

Since the graph passes through the origin $(0,0)$, the function is of the form $y = A\sin(\omega x)$. Substituting $A = 5$ and $\omega=\frac{3\pi}{13}$, we get $y = 5\sin\left(\frac{3\pi}{13}x\right)$.