V2EX quadrant iii

Quadrant III

释义 Definition

Quadrant III(第三象限):在直角坐标平面中,x < 0 且 y < 0 的区域(通常位于左下方)。常用于解析几何、三角函数与单位圆中描述点或角所在的位置。(“quadrant”也可泛指“四分之一的区域/部分”。)

发音 Pronunciation (IPA)

/kwdrnt θri/

例句 Examples

The point \((-2, -5)\) lies in Quadrant III.
点 \((-2, -5)\) 位于第三象限。

Because both sine and cosine are negative in Quadrant III, the reference angle helps determine the exact angle.
由于在第三象限中正弦和余弦都为负,使用参考角有助于确定精确角度。

词源 Etymology

quadrant 来自拉丁语 quadrans,意为“四分之一”(与 quattuor “四”有关),原本指圆或平面被分成四份中的一份;在笛卡尔坐标系里,平面被 x 轴与 y 轴分成四个区域,于是形成 Quadrant IIV 的命名方式。III 是罗马数字,表示 “3”。

相关词 Related Words

文学与著名作品 Literary Works

  • James Stewart, Calculus(《微积分》)在三角函数、单位圆与图像分析中常出现 “Quadrant III”。
  • Ron Larson, Precalculus(《预备微积分》)讲解象限、角度与三角函数符号规律时使用该术语。
  • George B. Thomas et al., Thomas’ Calculus(《托马斯微积分》)在坐标几何与函数图像相关章节中常见。
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