cos^-1(x) - Wolfram|Alpha

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Input

cos^(-1)(x)

Plot

Plot

Plot

Alternate form

1/2 (π - 2 sin^(-1)(x))

π/2 + i log(sqrt(1 - x^2) + i x)

Root

x = 1

Properties as a real function

Domain

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

Range

{y element R : 0<=y<=π}

Injectivity

injective (one-to-one)

Derivative

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

Indefinite integral

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

Global minimum

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

Global maximum

$max{cos^(-1)(x)} = π at x = -1$

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