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Implement sin(x) with precision constraints

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MediumSoftware EngineerTechnical ScreenCoding & Algorithms

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This question evaluates understanding of numerical methods, floating-point arithmetic, and algorithmic implementation in the Coding & Algorithms domain by requiring an approximation of the sine function under explicit error bounds.

Coding Question: Implement sin(x)

Implement a function that returns an approximation of the trigonometric sine function.

Function signature

  • Input: a real number x (in radians)
  • Output: sin(x) as a floating-point number

Restrictions

  • Do not call library trig functions (e.g., sin, cos, tan).
  • You may use basic arithmetic operations and constants.

Accuracy requirement

  • Your result must satisfy: (|\text{ans} - \sin(x)| \le \varepsilon)
  • Assume the interviewer provides a specific ε (e.g., 1e-6).

Notes

  • You may assume IEEE-754 double behavior.
  • Consider how your implementation behaves for very large magnitude x and near special points (e.g., around 0, π, π/2).

Follow-up questions

  • After writing a straightforward version, describe how you would **optimize** it (time and/or numerical stability).
  • In real systems, how would you further **engineer** this function for performance and reliability (e.g., handling large `|x|`, speed, testing, edge cases)?