Answer: π/3, 2π/3, 4π/3, 5π/3.
- A π/3, 2π/3, 4π/3, 5π/3
- B π/3, π/3 + π, missing two of the four valid solutions
- C π/6, 5π/6, using the wrong reference angle
- D π/3, treating it as the single unique solution
Correct answer: A. π/3, 2π/3, 4π/3, 5π/3
Explanation: tan²θ=3 → tanθ=±√3. Reference angle α=π/3. tanθ=+√3 in Q<sub>1</sub>, Q<sub>3</sub>: θ=π/3, 4π/3. tanθ=−√3 in Q2, Q4: θ=2π/3, 5π/3. Four solutions: π/3, 2π/3, 4π/3, 5π/3. General form: nπ±π/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