2026 · Q47
What is the ratio of the greatest value of sin²x + 2 (where 0 ≤ x ≤ π/2) to its least value?
Elementary MathematicsTrigonometry
- A2
- B3/2
- C3
- D1/2
Explanation
On [0, π/2], sin²x ranges from 0 (at x = 0) to 1 (at x = π/2). Therefore sin²x + 2 ranges from 2 to 3. The ratio of the greatest value to the least value is 3/2, option B.