1. The problem asks: In the curve $y = \tan 4x$, what is its period? 2. The general formula for the period of $y = \tan bx$ is $\frac{\pi}{|b|}$. 3. Here, $b = 4$, so the period is: $$\text{Period} = \frac{\pi}{4} \approx 0.7854$$ 4. Among the given options, the closest value to $0.7854$ is $0.51$, but none exactly match $\frac{\pi}{4}$. The correct period is $\frac{\pi}{4}$. Final answer: The period of $y = \tan 4x$ is $\frac{\pi}{4}$ (approximately 0.7854).