Evaluate tan π/2

To evaluate \( \tan(\pi/2) \), let's proceed step by step.

1. **Understanding the tangent function**:
The tangent of an angle \( \theta \) is defined as:
\[
\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}
\]
This means the tangent function is undefined wherever \( \cos(\theta) = 0 \), as division by zero is not possible.

2. **Value of cosine and sine at \( \pi/2 \)**:
- From the unit circle, at \( \theta = \pi/2 \) (90 degrees):
- \( \sin(\pi/2) = 1 \)
- \( \cos(\pi/2) = 0 \)

3. **Substituting into the formula**:
Substituting these values into the tangent formula:
\[
\tan(\pi/2) = \frac{\sin(\pi/2)}{\cos(\pi/2)} = \frac{1}{0}
\]

4. **Conclusion**:
Division by zero is undefined in mathematics. Hence, \( \tan(\pi/2) \) is undefined.

**Final Answer**:
\( \tan(\pi/2) \) is undefined.