2021 · Q57
If sin θ cos θ = k, where 0 ≤ θ ≤ π/2, then which one of the following is correct?
Elementary MathematicsTrigonometry
- A0 ≤ k ≤ 1
- B0 ≤ k ≤ 0.5 only
- C0.5 ≤ k ≤ 1 only
- D0 < k < 1
Explanation
sinθcosθ = (1/2)sin2θ, and for 0 ≤ θ ≤ π/2 the value of sin2θ ranges over [0, 1]. Hence 0 ≤ k ≤ 0.5 exactly — option B is the precise statement (option A is implied but looser). Hence option B.