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📐 Mathematics  ·  Trigonometric Functions  ·  JEE

Solve: 2cos²θ - 3cosθ + 1 = 0. Find all solutions in [0, 2π].

Answer: 0, π/3, 5π/3, 2π.

  • A 0, π/3, 5π/3, 2π
  • B 0, π/3, π
  • C π/3, π, 5π/3
  • D 0, 2π/3, 4π/3

Correct answer: A. 0, π/3, 5π/3, 2π

Explanation: Quadratic factoring: (2cosθ−1)(cosθ−1)=0. cosθ=1/2 → Q<sub>1</sub>: θ=π/3, Q4: θ=5π/3. cosθ=1 → θ=0 and θ=2π (boundary). All four solutions in [0,2π]: 0, π/3, 5π/3, 2π.

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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