Evaluate numerically:

Evaluate to high precision:

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

CotDegrees can take complex number inputs:

Evaluate CotDegrees efficiently at high precision:

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

Or compute average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix CotDegrees function using MatrixFunction:

Values of CotDegrees at fixed points:

CotDegrees has exact values at rational multiples of 60 degrees:

Values at infinity:

Simple exact values are generated automatically:

More complicated cases require explicit use of FunctionExpand:

Zeros of CotDegrees:

Find one zero using Solve:

Substitute in the result:

Visualize the result:

Singular points of CotDegrees:

Plot the CotDegrees function:

Plot over a subset of the complexes:

Plot the real part of CotDegrees:

Plot the imaginary part of CotDegrees:

Polar plot with CotDegrees:

CotDegrees is a periodic function with a period of :

Check this with FunctionPeriod:

Real domain of CotDegrees:

Complex domain:

CotDegrees achieves all real values:

The range for complex values:

CotDegrees is an odd function:

CotDegrees has the mirror property :

CotDegrees is not an analytic function:

However, it is meromorphic:

CotDegrees is monotonic in a specific range:

CotDegrees is not injective:

CotDegrees is surjective:

CotDegrees is neither non-negative nor non-positive:

CotDegrees has both singularities and discontinuities in points multiple to 180:

CotDegrees is neither convex nor concave:

CotDegrees is convex for x in [0,90]:

TraditionalForm formatting:

First derivative:

Higher derivatives:

Formula for the derivative:

Compute the indefinite integrals of CotDegrees via Integrate:

Definite integral for CotDegrees over a period:

More integrals:

Find the Taylor expansion using Series:

Plot the first three approximations for CotDegrees around :

Asymptotic expansion at a singular point:

CotDegrees can be applied to power series:

Double-angle formula using TrigExpand:

Angle sum formula:

Multiple‐angle expressions:

Recover the original expression using TrigReduce:

Convert sums to products using TrigFactor:

Convert to exponentials using TrigToExp:

Representation through TanDegrees:

Representation through SinDegrees and CosDegrees:

Representation through SecDegrees and CscDegrees:

Given , find the CotDegrees of the angle using the identity :

Find the missing adjacent side length of a right triangle if the opposite side is 5 and the angle is 30 degrees:

Calculate the CotDegrees value of 105 degrees using the sum and difference formulas:

Compare with the result of direct calculation:

Calculate the CotDegrees value of 15 degrees using the half-angle formula :

Compare this result with directly calculated CotDegrees:

Simplify trigonometric expressions:

Verify trigonometric identities:

Solve a basic trigonometric equation:

Solve trigonometric equations including other trigonometric functions:

Solve trigonometric equations with condition:

Solve this trigonometric inequality:

Solve this trigonometric inequality including other trigonometric functions:

Generate a plot over the complex argument plane:

Addition theorem for CotDegrees function: