Answer: 3.
- A 3
- B 4
- C 1
- D 0
Correct answer: A. 3
Explanation: Rewrite using cos²θ=1−sin²θ: 3sin²θ+4(1−sin²θ)=4−sin²θ. Since 0≤sin²θ≤1, the minimum value occurs at sin²θ=1 (maximum subtraction): 4−1=3. The maximum is 4 (at sinθ=0). Min=3.
Unit circle with standard angles 0, 30, 45, 60, 90 degrees; at 45 degrees the point is (cos45, sin45) = (1/sqrt2, 1/sqrt2).
Concept context
Ratios, identities, and applications in triangles