ArcCscDegrees
gives the arc cosecant in degrees of the complex number .
Details
![](Files/ArcCscDegrees.en/details_1.png)
- 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 allBasic Examples (7)
Calculate the angle ABC of this right triangle:
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)
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:
Singular points of ArcCscDegrees:
ArcCscDegrees is not differentiable at these points:
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 :
ArcCscDegrees achieves all real values from the interval except
:
ArcCscDegrees is an odd function:
ArcCscDegrees is not an analytic function:
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:
Integration (2)
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:
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:
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