為什麼反三角函數的前綴是arc？arc的意思是什麼？

01-08

百度，維基後均未果，求指點。

arc就是「弧」的意思。

反三角函數的作用，直觀地理解就是「抵消」原三角函數對弧施加的作用，例如

$arcsin(sin(frac{pi}{6} )) = frac{pi}{6}$

另一種理解是：

arcsin(x)計算的是這樣一個弧，它的「sin值等於x」，也就是說一個值為k的弧，sin(k) = x，那麼arcsin(x) = k.

用英文說：

arcsin of x is the arc whose sin is x.

在 @王大鎚的提點下，去搜索了英文維基，果然有解釋。

Etymology of the arc- prefix
When measuring in radians, an angle of θ radians will correspond to an arc whose length is rθ, where r is the radius of the circle. Thus, in the unit circle, "the arc whose cosine is x" is the same as "the angle whose cosine is x", because the length of the arc of the circle in radii is the same as the measurement of the angle in radians.

https://en.wikipedia.org/wiki/Inverse_trigonometric_functions

所以還是要提高自己的姿勢水平啊…