Asha plots tan x for x from 0 to 4π. How many asymptotes does the graph have in that range? …

Step 1. The asymptotes. At $\dfrac{\pi}{2}$, $\dfrac{3\pi}{2}$, $\dfrac{5\pi}{2}$ and $\dfrac{7\pi}{2}$. The next, $\dfrac{9\pi}{2} = 14.14$, is beyond $4\pi = 12.57$. That is $4$ asymptotes.

Step 2. Period. The tangent repeats every $\pi = 3.142$ rad.

Step 3. The huge value. np.tan(np.pi / 2) prints 1.633123935319537e+16, which is $1.6 \times 10^{16}$.