Evaluate to high precision:

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

Evaluate for complex arguments:

Evaluate SecDegrees 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 SecDegrees function using MatrixFunction :

Values of SecDegrees at fixed points:

SecDegrees has exact values at rational multiples of 30 degrees:

Values at infinity:

Simple exact values are generated automatically:

More complicated cases require explicit use of FunctionExpand :

Singular points of SecDegrees :

Local extrema of SecDegrees :

Find a local minimum of SecDegrees as the root of (dTemplateBox[{x}, SecDegrees])/(d x)=0 in the minimum's neighborhood:

Substitute in the result:

Visualize the result:

Plot the SecDegrees function:

Plot over a subset of the complexes:

Plot the real part of SecDegrees :

Plot the imaginary part of SecDegrees :

Polar plot with SecDegrees :

SecDegrees is a periodic function with a period of :

Check this with FunctionPeriod :

The real domain of SecDegrees :

Complex domain:

SecDegrees achieves all real values except the open interval :

The range for complex values:

SecDegrees is an even function:

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

SecDegrees is not an analytic function:

However, it is meromorphic:

SecDegrees is monotonic in a specific range:

SecDegrees is not injective:

SecDegrees is not surjective:

SecDegrees is neither non-negative nor non-positive:

It has both singularity and discontinuity when x is a multiple of 90:

Neither convex nor concave:

It is convex for x in [-90,90]:

TraditionalForm formatting:

First derivative:

Higher derivatives:

Formula for the ^(th) derivative:

Compute the indefinite integral of SecDegrees via Integrate :

Definite integral of SecDegrees over a period is 0:

More integrals:

Find the Taylor expansion using Series :

Plot the first three approximations for SecDegrees around :

Asymptotic expansion at a singular point:

SecDegrees can be applied to power series:

Double-angle formula using TrigExpand :

Angle sum formula:

Multiple‐angle expressions:

Convert sums to products using TrigFactor :

Convert to complex exponentials:

Representation through CosDegrees :

Representation through SinDegrees :

Representations through SinDegrees and TanDegrees :

Given , find the SecDegrees of the angle using the formula :

Find the missing adjacent side length of a right triangle with hypotenuse 5 given the angle is 30 degrees:

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

Compare with the result of direct calculation:

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:

Automatically label different trigonometric functions: