Step-by-Step Solution
Key Concept: The period of sin²θ can be found using the double angle identity: sin²θ = (1 - cos2θ)/2. Since cos2θ has period π, sin²θ must also have period π (not 2π).
<p><strong>Step 1:</strong> Apply the double angle identity for cos2θ:</p><p>sin²θ = (1 - cos2θ)/2</p><p><strong>Step 2:</strong> Identify the period of the right side. The constant term 1/2 doesn't affect periodicity. The cosine function cos2θ has period 2π/2 = π.</p><p><strong>Step 3:</strong> Verify by checking: sin²(θ + π) = [sin(θ + π)]² = [-sinθ]² = sin²θ ✓</p><p><strong>Step 4:</strong> Verify π is the smallest such period: sin²(θ + π/2) = [sin(θ + π/2)]² = cos²θ ≠ sin²θ (in general)</p><p>∴ The period of sin²θ is <strong>π</strong></p>
Correct Answer: B