Cos-1 Calculator

Cos-1, officially known as arccosine or inverse cosine, is a trigonometric function that takes a numeric ratio and returns the corresponding angle. It essentially reverses what the standard cosine function does. While cosine takes an angle and gives you the ratio of the adjacent side to the hypotenuse, cos-1 takes that ratio and gives you back the original angle.

To invert the cosine function algebraically, you restrict the domain of the standard cosine function to the interval [0, π] so that it becomes strictly monotonic and invertible. You then swap the input and output variables, resulting in y = arccos(x). Graphically, this is achieved by reflecting the cosine curve across the diagonal line y = x.

No, the inverse cosine function is neither even nor odd, meaning it is not antisymmetric. While functions like arcsine possess antisymmetry such that arcsin(-x) = -arcsin(x), arccosine follows a different identity: arccos(-x) = π - arccos(x). This geometric property ensures that the output angles remain strictly within the principal range of 0 to pi radians.

To calculate the inverse cosine of one half, you evaluate cos⁻¹(0.5). Recognizing standard unit circle values, you look for the angle between 0 and 180 degrees whose x-coordinate is 0.5. This evaluation yields exactly 60 degrees, or equivalently, π/3 radians, which frequently appears in physics and vector math problems.