Arc cosine of a complex number
Calculator for calculating the inverse cosine of a complex number
The function returns the angle, which is the arc cosine of a complex number representing a cosine. The angle is given in radians.
To perform the calculation, enter the complex number. Then click on the 'Calculate' button.
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Description of the arccosine for real numbers
The arc cosine ( Arccos or Acos ) is the inverse of the cosine function. As their inverse functions, the arc cosine returns the associated angle from the cosine value.
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: \(\displaystyle \ \ \frac{0.3 · 180 }{3.14} ≈ 17.189 °\)
More complex functions
Absolute value (abs) • Angle • Conjugate • Division • Exponent • Logarithm to base 10 • Multiplication • Natural logarithm • Polarform • Power • Root • Reciprocal • Square root •Cosh • Sinh • Tanh •
Acos • Asin • Atan • Cos • Sin • Tan •
Airy function • Derivative Airy function •
Bessel-I • Bessel-Ie • Bessel-J • Bessel-Je • Bessel-K • Bessel-Ke • Bessel-Y • Bessel-Ye •
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