ArcCscDegrees

ArcCscDegrees[z]

gives the arc cosecant in degrees of the complex number .

Details

  • ArcCscDegrees, along with other inverse trigonometric and trigonometric functions, is studied in high-school geometry courses and is also used in many scientific disciplines.
  • All results are given in degrees.
  • For real z outside the interval to , the results are always in the range to , excluding 0.
  • ArcCscDegrees[z] returns the angle in degrees for which the ratio of the hypotenuse to the opposite side of a right triangle is .
  • For certain special arguments, ArcCscDegrees automatically evaluates to exact values.
  • ArcCscDegrees can be evaluated to arbitrary numerical precision.
  • ArcCscDegrees automatically threads over lists.
  • ArcCscDegrees[z] has a branch cut discontinuity in the complex plane running from to .
  • ArcCscDegrees can be used with Interval, CenteredInterval and Around objects.
  • Mathematical function, suitable for both symbolic and numerical manipulation.

Examples

open allclose all

Basic Examples  (7)

Results are in degrees:

Calculate the angle ABC of this right triangle:

Calculate by hand:

The numerical value of this angle:

Solve an inverse trigonometric equation:

Solve an inverse trigonometric inequality:

Apply ArcCscDegrees to the following list:

Plot over a subset of the reals:

Asymptotic expansion at Infinity:

Scope  (38)

Numerical Evaluation  (6)

Evaluate numerically:

Evaluate to high precision:

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

Evaluate for complex arguments:

Evaluate ArcCscDegrees 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 ArcCscDegrees function using MatrixFunction:

Specific Values  (5)

Values of ArcCscDegrees at fixed points:

Simple exact values are generated automatically:

Values at infinity:

Singular points of ArcCscDegrees:

ArcCscDegrees is not differentiable at these points:

Find the value of satisfying equation :

Substitute in the value:

Visualize the result:

Visualization  (4)

Plot the ArcCscDegrees function:

Plot over a subset of the complexes:

Plot the real part of ArcCscDegrees:

Plot the imaginary part of ArcCscDegrees:

Polar plot with ArcCscDegrees:

Function Properties  (11)

ArcCscDegrees is defined for all real values except from the interval :

Complex domain:

ArcCscDegrees achieves all real values from the interval except :

The range for complex values:

ArcCscDegrees is an odd function:

ArcCscDegrees is not an analytic function:

Nor is it meromorphic:

ArcCscDegrees is monotonic in a specific range:

ArcCscDegrees is injective:

ArcCscDegrees is not surjective:

ArcCscDegrees is neither non-negative nor non-positive:

It has both singularity and discontinuity for x in [-1,1]:

ArcCscDegrees is neither convex nor concave:

ArcCscDegrees is convex for x in [1,∞):

TraditionalForm formatting:

Differentiation  (3)

First derivative:

Higher derivatives:

Formula for the ^(th) derivative:

Integration  (2)

Indefinite integral of ArcCscDegrees:

Definite integral of ArcCscDegrees over the interval :

Series Expansions  (4)

Find the Taylor expansion using Series:

Plots of the first three approximations for ArcCscDegrees around :

Find series expansions at branch points and branch cuts:

Asymptotic expansion at a singular point:

ArcCscDegrees can be applied to power series:

Function Identities and Simplifications  (2)

Simplify expressions involving ArcCscDegrees:

Use TrigToExp to express through logarithms and square roots:

Function Representations  (1)

Represent using ArcSinDegrees:

Applications  (6)

Solve inverse trigonometric equations:

Solve an inverse trigonometric equation with a parameter:

Use Reduce to solve inequalities involving ArcCscDegrees:

Numerically find a root of a transcendental equation:

Plot the function to check if the solution is correct:

Plot the real and imaginary parts of ArcCscDegrees:

Different combinations of ArcCscDegrees with trigonometric functions:

Properties & Relations  (6)

Compositions with the inverse trigonometric functions:

Use PowerExpand to disregard multivaluedness of the ArcCscDegrees:

Alternatively, evaluate under additional assumptions:

Use FunctionExpand to convert trigs of arctrigs into an algebraic function:

Simplify result:

This shows the branch cut of the ArcCscDegrees function:

ArcCscDegrees gives the angle in degrees, while ArcCsc gives the same angle in radians:

FunctionExpand applied to ArcCscDegrees generates expressions in trigonometric functions in radians:

ExpToTrig applied to the outputs of TrigToExp will generate trigonometric functions in radians:

Neat Examples  (2)

Solve trigonometric equations involving ArcCscDegrees:

Numerical value of this angle in degrees:

Plot ArcCscDegrees at integer points:

Wolfram Research (2024), ArcCscDegrees, Wolfram Language function, https://reference.wolfram.com/language/ref/ArcCscDegrees.html.

Text

Wolfram Research (2024), ArcCscDegrees, Wolfram Language function, https://reference.wolfram.com/language/ref/ArcCscDegrees.html.

CMS

Wolfram Language. 2024. "ArcCscDegrees." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ArcCscDegrees.html.

APA

Wolfram Language. (2024). ArcCscDegrees. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ArcCscDegrees.html

BibTeX

@misc{reference.wolfram_2024_arccscdegrees, author="Wolfram Research", title="{ArcCscDegrees}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/ArcCscDegrees.html}", note=[Accessed: 24-November-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_arccscdegrees, organization={Wolfram Research}, title={ArcCscDegrees}, year={2024}, url={https://reference.wolfram.com/language/ref/ArcCscDegrees.html}, note=[Accessed: 24-November-2024 ]}