Arccos(x), cos-1(x), inverse cosine function.
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).
arccos 1 = cos-1 1 = 0 rad = 0°
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 |
x | arccos(x) (rad) |
arccos(x) (°) |
---|---|---|
-1 | π | 180° |
-√3/2 | 5π/6 | 150° |
-√2/2 | 3π/4 | 135° |
-1/2 | 2π/3 | 120° |
0 | π/2 | 90° |
1/2 | π/3 | 60° |
√2/2 | π/4 | 45° |
√3/2 | π/6 | 30° |
1 | 0 | 0° |