Find tan 89° to two decimal places with a calculator or Python.

Step 1. The value. $\tan 89^\circ = 57.29$.

Step 2. Closer still. $\tan 89.9^\circ$ is about $573$ and $\tan 89.99^\circ$ is about $5730$. The values grow without any limit.

Step 3. Why. $\tan A = \dfrac{\sin A}{\cos A}$. Near $90^\circ$, $\sin A$ is close to $1$, but $\cos A$ is close to $0$. Dividing by a smaller and smaller number gives a bigger and bigger answer.

Step 4. At 90°. $\cos 90^\circ = 0$, and division by $0$ has no answer.