1/2 (π - 2 sin^(-1)(x))

π/2 + i log(sqrt(1 - x^2) + i x)

x = 1

{x element R : -1<=x<=1}

{y element R : 0<=y<=π}

injective (one-to-one)

π - sqrt(2) sqrt(x + 1) - (x + 1)^(3/2)/(6 sqrt(2)) - (3 (x + 1)^(5/2))/(80 sqrt(2)) - (5 (x + 1)^(7/2))/(448 sqrt(2)) - (35 (x + 1)^(9/2))/(9216 sqrt(2)) + O((x + 1)^5) (Puiseux series)

π/2 - x - x^3/6 - (3 x^5)/40 + O(x^6) (Taylor series)

(-1)^ceiling(arg(x - 1)/(2 π)) (i sqrt(2) sqrt(x - 1) - (i (x - 1)^(3/2))/(6 sqrt(2)) + (3 i (x - 1)^(5/2))/(80 sqrt(2)) - (5 i (x - 1)^(7/2))/(448 sqrt(2)) + (35 i (x - 1)^(9/2))/(9216 sqrt(2)) + O((x - 1)^(11/2)))

1/2 i (2 log(x) + log(4)) - i/(4 x^2) - (3 i)/(32 x^4) + O((1/x)^6) (generalized Puiseux series)

d/dx(cos^(-1)(x)) = -1/sqrt(1 - x^2)

integral cos^(-1)(x) dx = x cos^(-1)(x) - sqrt(1 - x^2) + constant

min{cos^(-1)(x)} = 0 at x = 1

max{cos^(-1)(x)} = π at x = -1

cos^(-1)(x) = cd^(-1)(x|0)

cos^(-1)(x) = cn^(-1)(x|0)

cos^(-1)(x) = sec^(-1)(1/x)

integral_0^1 cos^(-1)(x) dx≈1.00000000000...

integral_(-1)^0 cos^(-1)(x) dx≈2.14159...

cos^(-1)(x) = π/2 - sum_(k=0)^∞ (x^(1 + 2 k) (1/2)_k)/(k! + 2 k k!) for abs(x)<1

cos^(-1)(x) = sqrt(2 - 2 x) sum_(k=0)^∞ (2^(-k) (1 - x)^k (1/2)_k)/(k! + 2 k k!) for abs(-1 + x)<2

cos^(-1)(x) = π - sqrt(2) sqrt(1 + x) sum_(k=0)^∞ (2^(-k) (1 + x)^k (1/2)_k)/(k! + 2 k k!) for abs(1 + x)<2

cos^(-1)(x) = integral_x^1 1/sqrt(1 - t^2) dt

cos^(-1)(x) = π/2 + (i x)/(4 π^(3/2)) integral_(-i ∞ + γ)^(i ∞ + γ) (1 - x^2)^(-s) Γ(1/2 - s)^2 Γ(s) Γ(1/2 + s) ds for (0<γ<1/2 and abs(arg(1 - x^2))<π)

cos^(-1)(x) = π/2 + (i x)/(4 π^(3/2)) integral_(-i ∞ + γ)^(i ∞ + γ) ((-x^2)^(-s) Γ(1/2 - s)^2 Γ(s))/Γ(3/2 - s) ds for (0<γ<1/2 and abs(arg(-x^2))<π)

cos^(-1)(x) = π/2 - (x sqrt(1 - x^2))/(1 + Κ_(k=1)^∞ (-2 x^2 floor((1 + k)/2) (-1 + 2 floor((1 + k)/2)))/(1 + 2 k)) = π/2 - (x sqrt(1 - x^2))/(1 + -(2 x^2)/(3 - (2 x^2)/(5 - (12 x^2)/(7 - (12 x^2)/(9 + ...))))) for (x not element R or ((not 1<=x<∞) and (not -∞