“trigonometric series expansions”的概念、定义、翻译、参考文献-科学参考

trigonometric series expansions

Mathematics

For x measured in radians, the basic trigonometric functions sine and cosine can be expressed by the following series expansions, derived as Taylor series:

$\begin{array}{l} sin x = x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} + \dots + {(- 1)}^{k} \frac{x^{2 k + 1}}{(2 k + 1)!} + \dots, \\ cos x = 1 - \frac{x^{2}}{2!} + \frac{x^{4}}{4!} + \dots + {(- 1)}^{k} \frac{x^{2 k}}{(2 k)!} + \dots . \end{array}$

These series converge for all real and complex values of x.

单词	trigonometric series expansions
释义	trigonometric series expansions Mathematics For x measured in radians, the basic trigonometric functions sine and cosine can be expressed by the following series expansions, derived as Taylor series: $\begin{array}{l} sin x = x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} + \dots + {(- 1)}^{k} \frac{x^{2 k + 1}}{(2 k + 1)!} + \dots, \\ cos x = 1 - \frac{x^{2}}{2!} + \frac{x^{4}}{4!} + \dots + {(- 1)}^{k} \frac{x^{2 k}}{(2 k)!} + \dots . \end{array}$ These series converge for all real and complex values of x.
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