Answer
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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Recall the definition of tangent
The tangent function is defined as $$\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}
Step 3:: Analyze the special angle π/ 2
- $$\cos(\frac{\pi}{2}) = 0
- \sin(\frac{\pi}{2}) = 1
Step 4:: Calculate tan(π/ 2)
\tan(\frac{\pi}{2}) = \frac{\sin(\frac{\pi}{2})}{\cos(\frac{\pi}{2})} = \frac{1}{0}
Step 5:: Interpret the result
This means $$\tan(\frac{\pi}{2})$$ does not exist.
Division by zero is undefined.
Final Answer
Key Insight: At π/ 2 (90 degrees), the tangent function approaches infinity, but is not a defined real number.
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