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📐 Mathematics  ·  Trigonometric Functions  ·  JEE

The minimum value of 3 sin²θ + 4 cos²θ is:

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.

xy0 deg30 deg45 deg (1/sqrt2, 1/sqrt2)60 deg90 degcos45sin45

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

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