Built-in solutions

Python, 17 bytes

from math import* # asin, acos,atan

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Python, 18 bytes (supports all real values)

from cmath import* #asin,acos,atan

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Vyxal, 2 bytes each

∆S # Arcsine
∆C # Arccosine
∆T # Arctangent

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Thunno 2, 2 bytes each

Æs # arcsin
Æc # arccos
Æt # arctan

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JavaScript, 29 bytes

Math.asin
Math.acos
Math.atan

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Rust

f64::asin
f64::acos
f64::atan

APL(Dyalog Unicode), 1 bytes ^SBCS

○

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Left argument chooses function:

¯1○⍵ ⍝ asin
¯2○⍵ ⍝ acos
¯3○⍵ ⍝ atan

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13 bytes (reals only)

import."math"
// Asin
// Acos
// Atan

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19 bytes (includes complex numbers)

import."math/cmplx"
// Asin
// Acos
// Atan

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sclin, 14 bytes

sin_
cos_
tan_

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