Arccos definition

The arccosine of x is defined as the inverse cosine function of x when -1≤x≤1.

When the cosine of y is equal to x:

cos y = x

Then the arccosine of x is equal to the inverse cosine function of x, which is equal to y:

arccos x = cos^-1 x = y

(Here cos^-1 x means the inverse cosine and does not mean cosine to the power of -1).

Example

arccos 1 = cos^-1 1 = 0 rad = 0°

Graph of arccos

Arccos rules

Rule name	Rule
Cosine of arccosine	cos( arccos x ) = x
Arccosine of cosine	arccos( cos x ) = x + 2kπ, when k∈ℤ (k is integer)
Arccos of negative argument	arccos(-x) = π – arccos x = 180° – arccos x
Complementary angles	arccos x = π/2 – arcsin x = 90° – arcsin x
Arccos sum	arccos(α) + arccos(β) =    arccos( αβ – √(1-α2)(1-β2) )
Arccos difference	arccos(α) – arccos(β) =    arccos( αβ + √(1-α2)(1-β2) )
Arccos of sin of x	arccos( sin x ) =  –x – (2k+0.5)π
Sine of arccosine
Tangent of arccosine
Derivative of arccosine
Indefinite integral of arccosine