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  "tool_id": "sin",
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    "Real sine. The published engine is forward sin(θ). Opposite/hypotenuse is a local triangle convenience (hypotenuse > 0, opposite ≥ 0, opposite ≤ hypotenuse). Use Arcsin for the inverse API.",
    "Algebraic snap applies only when the reduced angle (mod 360°) is a listed identity such as 0°, 30°, 45°, 60°, 90°. Nearby floats, including 30.00000005°, keep IEEE-754 Math.sin."
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    "sin(0°) = 0; sin(30°) = 1/2; sin(90°) = 1; sin(150°) = 1/2; sin(180°) = 0; sin(−θ) = −sin(θ)."
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      "section": "Definitions and period of sine and cosine",
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      "supports": "sin(θ) on the real line; odd function; degree input converted via θ° × π/180",
      "kind": "reference"
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