SecDegrees
SecDegrees[θ]
gives the secant of degrees.
Details
![](Files/SecDegrees.en/details_1.png)
- SecDegrees and other trigonometric functions are studied in high-school geometry courses and are also used in many scientific disciplines.
- The argument of SecDegrees is assumed to be in degrees.
- SecDegrees of angle
is the ratio of the hypotenuse to the adjacent side of a right triangle:
- SecDegrees is related to CosDegrees by the identity
.
- For certain special arguments, SecDegrees automatically evaluates to exact values.
- SecDegrees can be evaluated to arbitrary numerical precision.
- SecDegrees automatically threads over lists.
- SecDegrees can be used with Interval, CenteredInterval and Around objects.
- Mathematical function, suitable for both symbolic and numerical manipulation.
Examples
open allclose allBasic Examples (6)
The argument is given in degrees:
Calculate SecDegrees of 45 Degree for a right triangle with unit sides:
Solve a trigonometric equation:
Scope (45)
Numerical Evaluation (5)
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:
Specific Values (6)
Values of SecDegrees at fixed points:
SecDegrees has exact values at rational multiples of 30 degrees:
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 in the minimum's neighborhood:
Visualization (4)
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:
Function Properties (13)
SecDegrees is a periodic function with a period of :
Check this with FunctionPeriod:
The real domain of SecDegrees:
SecDegrees achieves all real values except the open interval :
SecDegrees is an even function:
SecDegrees has the mirror property :
SecDegrees is not an analytic function:
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:
It is convex for x in [-90,90]:
TraditionalForm formatting:
Integration (3)
Compute the indefinite integral of SecDegrees via Integrate:
Definite integral of SecDegrees over a period is 0:
Series Expansions (3)
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:
Function Identities and Simplifications (5)
Double-angle formula using TrigExpand:
Convert sums to products using TrigFactor:
Function Representations (3)
Representation through CosDegrees:
Representation through SinDegrees:
Representations through SinDegrees and TanDegrees:
Applications (11)
Basic Trigonomometric Applications (2)
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:
Trigonomometric Identities (3)
Calculate the SecDegrees value of 105 degrees using the sum and difference formulas:
Compare with the result of direct calculation:
Trigonomometric Equations (2)
Trigonomometric Inequalities (2)
Properties & Relations (13)
Check that 1 degree is radians:
Basic parity and periodicity properties are automatically applied:
Simplify under assumptions on parameters:
Complicated expressions containing trigonometric functions do not simplify automatically:
Use FunctionExpand to express SecDegrees in terms of radicals:
Compositions with the inverse trigonometric functions:
Solve a trigonometric equation:
Numerically solve a transcendental equation:
Plot the function to check if the solution is correct:
The zeros of SecDegrees:
The poles of SecDegrees:
Calculate residue symbolically and numerically:
FunctionExpand applied to SecDegrees generates expressions in trigonometric functions in radians:
ExpToTrig applied to the outputs of TrigToExp will generate trigonometric functions in radians:
SecDegrees is a numeric function:
Possible Issues (1)
Neat Examples (5)
Trigonometric functions are ratios that relate the angle measures of a right triangle to the length of its sides:
Solve trigonometric equations:
Add some condition on the solution:
Some arguments can be expressed as a finite sequence of nested radicals:
Plot SecDegrees at integer points:
Text
Wolfram Research (2024), SecDegrees, Wolfram Language function, https://reference.wolfram.com/language/ref/SecDegrees.html.
CMS
Wolfram Language. 2024. "SecDegrees." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SecDegrees.html.
APA
Wolfram Language. (2024). SecDegrees. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SecDegrees.html