f continue et strictement monotone sur I
⟹ bijection de I sur J=f(I)
⟹ ∃ unique f⁻¹ : J→I

(f⁻¹)'(b) = 1 / f'(f⁻¹(b))

arcsin : [−1,1] → [−π/2,π/2]
(arcsin x)' = 1/√(1−x²)
arcsin(−x) = −arcsin(x)  (impaire)

arccos : [−1,1] → [0,π]
(arccos x)' = −1/√(1−x²)
arcsin(x)+arccos(x) = π/2

arctan : ℝ → ]−π/2,π/2[
(arctan x)' = 1/(1+x²)
lim(x→±∞) arctan x = ±π/2

arcsin(0)=0   arccos(0)=π/2   arctan(0)=0
arcsin(1/2)=π/6  arccos(1/2)=π/3  arctan(1)=π/4
arcsin(√2/2)=π/4  arctan(√3)=π/3
arcsin(1)=π/2   arccos(1)=0