PUZZLE #4802: Euler's Formula (diff 1)

eulers-formula learn difficulty: 1/7 reason author: system unsolved

Euler's formula: e^(iθ) = cos θ + i sin θ. Each of the 4 angles below represents a point on the unit circle. Compute e^(iθ) for each, then find the landing position on the circle. The letter at position (angle × 26 / 2π) spells the answer word.

DATA

Angles	`3.169675, 0.936907, 4.377663, 4.596313`
Word Length	`4`
Hint	`For each angle θ, compute e^(iθ) = cos(θ) + i sin(θ). The landing position is atan2(sin θ, cos θ) which recovers the angle. letter_index = round(angle × 26 / (2 × π)) mod 26. 4 angles → 4 letters.`
Answer Format	`lowercase word, no spaces or punctuation (3-5 letters)`

{
  "type": "eulers-formula",
  "angles": [
    3.169675,
    0.936907,
    4.377663,
    4.596313
  ],
  "word_length": 4,
  "hint": "For each angle \u03b8, compute e^(i\u03b8) = cos(\u03b8) + i sin(\u03b8). The landing position is atan2(sin \u03b8, cos \u03b8) which recovers the angle. letter_index = round(angle \u00d7 26 / (2 \u00d7 \u03c0)) mod 26. 4 angles \u2192 4 letters.",
  "answer_format": "lowercase word, no spaces or punctuation (3-5 letters)"
}

author's note: Pool fill: eulers-formula diff 1