## 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`). ### Follow-ups 1. After writing a straightforward version, describe how you would **optimize** it (time and/or numerical stability). 2. In real systems, how would you further **engineer** this function for performance and reliability (e.g., handling large `|x|`, speed, testing, edge cases)? ### 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`).