1. **State the problem:** Find the equation of the tangent line to the curve at the point $(3, \frac{5\pi}{2})$. 2. **Identify the curve:** The problem does not specify the curve explicitly, so we assume the curve is given or known. For example, if the curve is $y = f(x)$, we need $f(3) = \frac{5\pi}{2}$. 3. **Find the derivative:** The slope of the tangent line at $x=3$ is $m = f'(3)$. 4. **Use the point-slope form:** The equation of the tangent line is $$y - y_1 = m(x - x_1)$$ where $(x_1, y_1) = (3, \frac{5\pi}{2})$. 5. **Final equation:** Substitute $m$ and the point to get the tangent line equation. Since the curve is not specified, the exact equation cannot be found without $f(x)$ or $f'(x)$. **If you provide the function $f(x)$, I can compute the exact tangent line equation.**