Evaluate numerically:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Complex number input:

Evaluate efficiently at high precision:

Compute the elementwise values of an array using automatic threading:

Or compute the matrix InverseHaversine function using MatrixFunction:

Compute worst-case guaranteed intervals using Interval and CenteredInterval objects:

Or compute average-case statistical intervals using Around:

Values of InverseHaversine at fixed points:

The value of InverseHaversine at zero:

Find a value of for which using Solve:

Plot the InverseHaversine function:

Plot the real part of InverseHaversine[z]:

Plot the imaginary part of InverseHaversine[z]:

InverseHaversine is defined for all real values from the interval [0,1]:

InverseHaversine is defined for all complex values:

The real range:

InverseHaversine is not an analytic function:

Nor is it meromorphic:

InverseHaversine is non-decreasing over its real domain:

InverseHaversine is injective:

InverseHaversine is not surjective:

InverseHaversine is non-negative over its real domain:

InverseHaversine does have both singularity and discontinuity in (-∞,0] and [1,∞):

InverseHaversine is neither convex nor concave:

TraditionalForm formatting:

First derivative:

Higher derivatives:

Plot the higher derivatives:

The formula for the derivative:

Compute the indefinite integral using Integrate:

The definite integral:

More integrals:

Find the Taylor expansion using Series:

Plots of the first three approximations around :

The Taylor expansion at a generic point:

InverseHaversine can be applied to a power series: