Discussion
The Maclaurin expansion of \( \sin x \) begins
Answer: D
The derivatives at the origin cycle through \( 1, 0, -1, 0 \), so only odd powers survive and the signs alternate:
\[ \sin x \;=\; x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} - \cdots \;=\; x - \frac{x^{3}}{6} + \frac{x^{5}}{120} - \cdots \]
The even-power series with leading one is \( \cos x \), and the all-positive version is \( \sinh x \)
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