Answer: 2.
- A 1
- B 3/2
- C 2
- D 4
Correct answer: C. 2
Explanation: By symmetry sin(5π/8) = sin(3π/8) and sin(7π/8) = sin(π/8), and sin(3π/8) = cos(π/8). The sum is 2[sin²(π/8) + cos²(π/8)] = 2.
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