If \sin \theta \cos \theta=k, where 0 \leq \theta \leq \frac{\pi}{2} then which one of the following is correct?
- A. 0 \leq k \leq 1
- B. 0 \leq k \leq 0.5 <strong>ONLY</strong> ✓
- C. 0.5 \leq k \leq 1 <strong>ONLY</strong>
- D. 0 \lt k \lt 1
Correct Answer: B. 0 \leq k \leq 0.5 <strong>ONLY</strong>
Explanation
Since k = \sin \theta \cos \theta = \frac{\sin 2\theta}{2}, and the maximum value of \sin 2\theta for \theta \in [0, \frac{\pi}{2}] is 1 (and minimum is 0), the range for k is 0 \leq k \leq 0.5.
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