Evaluate numerically:

Evaluate to high precision:

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

TanDegrees can take complex number inputs:

Evaluate TanDegrees 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 TanDegrees function using MatrixFunction :

Values of TanDegrees at fixed points:

TanDegrees 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 TanDegrees :

Find one zero using Solve :

Substitute in the result:

Visualize the result:

Singular points of TanDegrees :

Plot the TanDegrees function:

Plot over a subset of the complexes:

Plot the real part of TanDegrees :

Plot the imaginary part of TanDegrees :

Polar plot with TanDegrees :

TanDegrees is a periodic function with a period of :

Check this with FunctionPeriod :

Real domain of TanDegrees :

Complex domain:

TanDegrees achieves all real values:

The range for complex values:

TanDegrees is an odd function:

TanDegrees has the mirror property tan(TemplateBox[{z}, Conjugate])=TemplateBox[{{tan, (, z, )}}, Conjugate]:

TanDegrees is not an analytic function:

However, it is meromorphic:

TanDegrees is monotonic in a specific range:

TanDegrees is not injective:

TanDegrees is surjective:

TanDegrees is neither non-negative nor non-positive:

TanDegrees has both singularities and discontinuities in points multiple to 90:

TanDegrees is neither convex nor concave:

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

TraditionalForm formatting:

First derivative:

Higher derivatives:

Formula for the ^(th) derivative:

Compute the indefinite integrals of TanDegrees via Integrate :

Definite integral of TanDegrees over a period is 0:

More integrals:

Find the Taylor expansion using Series :

Plot the first three approximations for TanDegrees around :

Asymptotic expansion at a singular point:

TanDegrees 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 CotDegrees :

Representation through SinDegrees and CosDegrees :

Representation through SecDegrees and CscDegrees :

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

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

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

Compare with the result of direct calculation:

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

Compare this result with directly calculated TanDegrees :

Simplify trigonometric expressions:

Verify trigonometric identities:

Solve a basic trigonometric equation:

Solve trigonometric equations including other trigonometric functions:

Solve trigonometric equations with conditions:

Solve this trigonometric inequality:

Solve this trigonometric inequality including other trigonometric functions:

Generate a plot over the complex argument plane:

The function has the limit zero as approaches :

Thus, its max limit is zero: