V2EX coterminal

Coterminal

定义 Definition

coterminal(共终的;同终点的):在数学(尤其三角学)中常指两个角(或弧)在标准位置下终边相同,也就是它们相差一个或多个整周:
\(\theta\) 与 \(\theta + 2k\pi\)(弧度)或 \(\theta + 360k^\circ\)(角度),其中 \(k\) 为整数。
(在更一般的语境中,也可指“共享同一终点/边界”的事物。)

发音 Pronunciation (IPA)

/kotmnl/

例句 Examples

Coterminal angles differ by 360 degrees.
共终角相差 360 度。

Because sine and cosine are periodic, any angle coterminal with \( \theta \) has the same sine and cosine values as \( \theta \).
由于正弦和余弦具有周期性,任何与 \( \theta \) 共终的角,其正弦值和余弦值都与 \( \theta \) 相同。

词源 Etymology

由前缀 co-(“共同、一起”)+ terminal(“终点的;末端的”)构成;terminal 源自拉丁语 terminus(“界限、终点”)。因此 coterminal 字面义为“共享同一终点/末端的”。

相关词 Related Words

文学与著作中的用例 Literary Works

  • Precalculus: Mathematics for Calculus(Stewart, Redlin, Watson)在“三角函数与角”的章节中讨论 coterminal angles
  • Trigonometry(Lial, Hornsby, Schneider)用 coterminal 解释同终边角与单位圆对应关系。
  • Calculus: Early Transcendentals(James Stewart)在三角函数回顾/附录部分常出现 coterminal angles 的概念。
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