Etymology of $\arccos$, $\arcsin$ & $\arctan$? Does anyone know the origin of the words $\arccos$, $\arcsin$ & $\arctan$? That is to say, why are they named like this? What connects "arc" with inverse?
 A: When measuring in radians, an angle of $\theta$ radians will correspond to an arc whose length is $r\theta$, 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 measurement of the length of the arc of the circle is the same as the measurement of the angle in radians.
I'll note that in Mexico, the functions were also called $\mathrm{ang\,sin}$, $\mathrm{ang\,cos}$, etc., meaning "angle whose sine is..." and "angle whose cosine is..." (rather than "arc whose ...").
A: Sine comes from sinew- bowstring and is the measurement up a bow from a bowstring laid on a surface, to where an arrow (nocked at center) touches the bow. Cosine is the complementing measure from the archer's arm (w elbow placed at center point.) The circle is the unit of one forearm, the string length- one forward one back (+1 thru -1.)
Since arc sine uses the bow vertically, I figured it was from using archer standing or the bow on a wall instead of a table. The archer's view, siting along arrow of measurement. Measures from the archer.
A: "Sine comes from sinew" 
I don't think so -- it comes from sinus, Latin for "bay", "pocket" or "curve." Compare to "sinuous"
