象限角

Multi tool use

「
第一象限」、「
第二象限」、「
第三象限」、「
第四象限」皆重定向至此。
關於科幻系列《星际旅行》中的
第一、二、三、四象限,詳見「
銀河系象限 (星空奇遇記)」。
象限角,又称象限(英文:Quadrant意思是一圓之四分一等份),是直角坐標系(笛卡爾坐標系)中,主要應用於三角學和複數的阿根圖(複平面)中的座標系。
設定
- x軸和y軸,或者,實數軸和虛數軸,數值均為正數的象限為「第一象限」。
- 「第一象限」的x軸為 0° 或 0 rad ,採用純數字的角度或弧度作度大小。(後者多過前者。)
- 由「第一象限」的 0° 或 0 rad 作逆時針轉動,為正增加角度度數。
- 一圈之內,共有四個象限,或 360° ,或 2π rad 。
象限表達
名稱 |
羅馬數字表示 |
明確表示 (X,Y)
|
第一象限 |
Ⅰ |
(+,+)
|
第二象限 |
Ⅱ |
(-,+)
|
第三象限 |
Ⅲ |
(-,-)
|
第四象限 |
Ⅳ |
(+,-)
|
三角學應用
當一個三角形的鄰邊、對邊和斜邊比例和象限位置改變時,最常用的三角函數數值:正弦、餘弦和正切,也會有不同的正負值。為了方便記憶,有一口訣以象限次序排列:ASTC 。
- 第一象限的 A 即是 All (全部皆正)。
- 第二象限的 S 即是 Sine (只有正弦為正)。
- 第三象限的 T 即是 Tangent (只有正切為正)。
- 第四象限的 C 即是 Cosine (只有餘弦為正)。
參阅
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