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弧度 - Wikipedia

弧度

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數學物理中,弧度的量度單位。它是國際單位制導出單位。單位弧度定義為圓周上長度等於半徑的圓弧與圓心構成的角。角度以弧度給出時,通常不寫弧度單位,或有時記為rad

一個完整的圓的弧度是2π,所以2π rad = 360°,1 rad = 180/π°(約57.29578°),1°=π/180 rad。以度數表示的角度,把數字乘以π/180便轉換成弧度;以弧度表示的角度,乘以180/π便轉換成度數。

微積分三角函數中,角度以弧度為單位,以獲得簡潔的結果。例如以弧度為單位,有如下簡單等式:

\lim_{h\to0}\frac{\sin h}h=1

從這等式可以推導出很多漂亮的數學等式。

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