The value of $\tan 90^\circ$ (or $\tan \frac{\pi}{2}$ radians) is undefined.

This is because the tangent function is defined as the ratio of the sine to the cosine:

$\tan \theta = \frac{\sin \theta}{\cos \theta}$

At $\theta = 90^\circ$, $\sin 90^\circ = 1$ and $\cos 90^\circ = 0$. Since division by zero is undefined, $\tan 90^\circ$ does not have a defined value.

Would you like more details on the behavior of the tangent function near 90 degrees?

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Here are 5 related questions to expand on this concept:

1. What happens to the value of $\tan \theta$ as $\theta$ approaches 90°?
2. How does the tangent function behave for angles beyond 90°?
3. What is the value of $\tan 0^\circ$?
4. Can you explain the relationship between the sine, cosine, and tangent functions?
5. How can you graphically interpret $\tan \theta$?

Tip: The tangent function has vertical asymptotes at odd multiples of 90°, indicating points where the function becomes undefined.