1. **State the problem:** We need to find the equation of a sinusoidal function with a given period of $\frac{8\pi}{3}$. 2. **Recall the formula for the period of sine or cosine:** $$T = \frac{2\pi}{b}$$ where $b$ is the frequency coefficient inside the function. 3. **Solve for $b$ using the given period:** $$b = \frac{2\pi}{T} = \frac{2\pi}{\frac{8\pi}{3}} = 2\pi \times \frac{3}{8\pi} = \frac{3}{4}$$ 4. **Write the general form of the function:** Assuming amplitude $a$ and no phase shift, the function is either $$y = a \sin\left(bx\right) \quad \text{or} \quad y = a \cos\left(bx\right)$$ 5. **If amplitude $a$ is known (e.g., from previous problem $a=4$), substitute:** $$y = 4 \sin\left( \frac{3}{4} x \right)$$ 6. **Final answer:** $$\boxed{y = 4 \sin\left( \frac{3}{4} x \right)}$$