1. The problem is to analyze the function $f(x) = \sin x$ over the interval $(0, 4\pi)$.\n\n2. The sine function is periodic with period $2\pi$, meaning it repeats every $2\pi$ units.\n\n3. Important properties:\n- The zeros of $\sin x$ occur at $x = k\pi$ for integers $k$.\n- The maximum value is 1 at $x = \frac{\pi}{2} + 2k\pi$.\n- The minimum value is -1 at $x = \frac{3\pi}{2} + 2k\pi$.\n\n4. On the interval $(0, 4\pi)$, the zeros are at $x = \pi, 2\pi, 3\pi, 4\pi$.\n\n5. The maxima occur at $x = \frac{\pi}{2}, \frac{5\pi}{2}$ with value 1.\n\n6. The minima occur at $x = \frac{3\pi}{2}, \frac{7\pi}{2}$ with value -1.\n\n7. The function oscillates between -1 and 1, crossing zero four times in this interval.\n\nFinal answer: The function $f(x) = \sin x$ on $(0,4\pi)$ has zeros at $\pi, 2\pi, 3\pi, 4\pi$, maxima 1 at $\frac{\pi}{2}, \frac{5\pi}{2}$, and minima -1 at $\frac{3\pi}{2}, \frac{7\pi}{2}$.