ACos - Arccosine (inverse cosine)

The calculator on this page calculates the inverse cosine for real numbers. Trigonometric functions for complex numbers can be found in the complex numbers section.

To calculate, enter the value of the cosine to which the angle should be calculated and click on the Calculate button. The unit of measurement for the result can be switched between degrees and radians.

Inverse cosine calculator Input Delete Entry Kosinus Unit of measure Degree Radiant Decimal places 0 1 2 3 4 6 8 10 Result Angle

Inverse cosine, scale in radians

Input

The value of the argument must be between -1 and +1.

Result

The result is given in degrees (full circle = 360°) or radians / radians (full circle = 2 π). The unit of measurement used is set to degrees or radians at the top of the menu.

Description of the arc cosine

The arc cosine (\( Arccos\) or \( Acos\)) is the inverse of the cosine function. It calculates the angle for a given cosine value. Acos(x) returns the corresponding angle in radians.

Calculation of the cosine value of an angle

The cosine is a trigonometric function related to a right triangle. In a right triangle, the cosine of an angle α is the ratio of the length of the adjacent side to the hypotenuse.

\(\displaystyle \cos(\alpha) = \frac{\text{Adjacent side}}{\text{Hypotenuse}}\)

Example

The assumption is a right-angled triangle with an adjacent side \(b = 6\) and the hypotenuse \(c = 20\). The cosine of α is calculated:

\(\displaystyle \cos(\alpha) = \frac{6}{20} = 0.3\)

Please note that the cosine value is always between -1 and 1, and an angle of 90 degrees has a cosine value of 0.

To calculate the angle from radians to degrees, the following formula is used:

\(\displaystyle \frac{\cos(\alpha) · 180 }{π} \)

For the example above: \(\displaystyle \ \ \frac{0.3 · 180 }{3.14} ≈ 17.189 °\)