Arccos(x) calculator. Inverse cosine calculator.
Arccos Calculator
Calculation History
| Input (x) | Output | Unit |
|---|
Arccos (inverse cosine) Calculator
Definition:
arccos(x) returns the angle whose cosine is x.
Range:
- In radians: 0 to π
- In degrees: 0° to 180°
Calculation:
Use JavaScript’s Math.acos(x) to compute the inverse cosine.
(Math.acos returns a value in radians by default.)
Conversion:
To convert radians to degrees, use:
degrees = radians × (180/π)
Note:
The input x must be within the interval [-1, 1].
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 |  |