Arccos(x) function

Arccos(x), cos^-1(x), inverse cosine function.

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.

For 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	cos (arcsin x) = sin (arccos x) = √1 - x2
Tangent of arccosine
Derivative of arccosine
Indefinite integral of arccosine	∫ arccos x dx = x arccos x - √1-x2 + C

Arccos table