Answer: (√5-1)/4.
- A (√5-1)/4
- B (√5+1)/4
- C (√5-1)/2
- D 1/4
Correct answer: A. (√5-1)/4
Explanation: Let θ=18°, so 5θ=90° → sin3θ=cos2θ. Expanding: 3sinθ−4sin³θ=1−2sin²θ. Set x=sinθ: 4x²+3x−1=0 (after dividing by sinθ≠0), giving x=(√5−1)/4. Answer: sin18°=(√5−1)/4.
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