Answer: 0.
- A n cosθ
- B 0
- C cosθ
- D 1
Correct answer: B. 0
Explanation: Phasor method: each term is Re(e^(i(θ+2πk/n))). Sum = Re(e<sup>iθ</sup>·Σe<sup>2πik/n</sup>) for k=0..n−1. The inner sum is the sum of all n-th roots of unity = 0. Therefore total sum = 0 for all θ.
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