What is inverse trigonometric functions?

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loo this following link https://byjus.com/maths/inverse-trigonometric-functions/

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What is mean by closed bracket and open bracket in inverse trigonometric functions and function please elaborate deeply with examples

{cos}^{- 1} (cos (- 5)) + {sin}^{- 1} (sin (6)) - {tan}^{- 1} (tan (12))

\begin{matrix} I n v e r s e T r i g o n o m e t r i c & D o m a i n & R a n g e F u n c t i o n y = s i n^{- 1} x & x ϵ [- 1, 1] & y ϵ [\frac{- π}{2}, \frac{π}{2}] y = c o s^{- 1} x & x ϵ [- 1, 1] & y ϵ [0, π] y = t a n^{- 1} x & x ϵ R & y ϵ (\frac{- π}{2}, \frac{π}{2}) y = c o t^{- 1} x & x ϵ R & y ϵ (0, π) y = s e c^{- 1} x & x ϵ R - (- 1, 1) & y ϵ [0, π] - {\frac{π}{2}} y = c o s e c^{- 1} x & x ϵ R - (- 1, 1) & y ϵ [\frac{- π}{2}, \frac{π}{2}] \end{matrix}

s i n^{- 1} x = | x - a |

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