Formulas of inverse trigonometric functions

Inverse trigonometric functions are mathematical functions that are inverse to trigonometric functions.


Table of inverse trigonometric functions

Function Domain Range
arcsinx [-1;1] [-π2; π2]
arcosx [-1;1] [0;π]
arctgx (-∞;∞) [-π2; π2]
arcctgx (-∞;∞) (0;π)

Properties of inverse trigonometric functions

sin(arcsinx)=x -1 ≤ x ≤ 1
cos(arccosx)=x -1 ≤ x ≤ 1
arcsin(sinx)=x -π2 ≤ x ≤ π2
arccos(cosx)=x 0 ≤ x ≤ π
tg(arctgx)=x x — any
ctg(arcctgx)=x x — any
arctg(tgx)=x -π2 ≤ x ≤ π2
arcctg(ctgx)=x 0 < x < π
arcsin(- x)= - arcsinx -1 ≤ x ≤ 1
arccos(- x)= π - arccosx -1 ≤ x ≤ 1
arctg(- x)= - arctgx x — any
arcctg(- x)= π - arcctgx x — any
arcsinx + arccosx = π2 -1 ≤ x ≤ 1
arctgx + arcctgx = π2 x — any
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