ArcCotDegrees
gives the arc cotangent in degrees of the complex number .
Details
![](Files/ArcCotDegrees.en/details_1.png)
- ArcCotDegrees, 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
, the results are always in the range
to
, excluding 0.
- ArcCotDegrees[z] returns the angle
in degrees for which the ratio of the adjacent side to the opposite side of a right triangle is
.
- For certain special arguments, ArcCotDegrees automatically evaluates to exact values.
- ArcCotDegrees can be evaluated to arbitrary numerical precision.
- ArcCotDegrees automatically threads over lists.
- ArcCotDegrees[z] has a branch cut discontinuity in the complex
plane running from
to
.
- ArcCotDegrees 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 BAC of this right triangle:
The numerical value of this angle:
Solve an inverse trigonometric equation:
Solve an inverse trigonometric inequality:
Apply ArcCotDegrees to the following list:
Plot over a subset of the reals:
Asymptotic expansion at Infinity:
Scope (39)
Numerical Evaluation (6)
The precision of the output tracks the precision of the input:
Evaluate for complex arguments:
Evaluate ArcCotDegrees 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 ArcCotDegrees function using MatrixFunction:
Specific Values (5)
Values of ArcCotDegrees at fixed points:
Simple exact values are generated automatically:
Singular points of ArcCotDegrees:
Visualization (4)
Plot the ArcCotDegrees function:
Plot over a subset of the complexes:
Plot the real part of ArcCotDegrees:
Plot the imaginary part of ArcCotDegrees:
Polar plot with ArcCotDegrees:
Function Properties (12)
ArcCotDegrees is defined for all real values:
ArcCotDegrees achieves all real values except 0 from the interval :
ArcCotDegrees is an odd function:
ArcCotDegrees has the mirror property :
ArcCotDegrees is not an analytic function:
ArcCotDegrees is neither non-decreasing nor non-increasing:
ArcCotDegrees is injective:
ArcCotDegrees is not surjective:
ArcCotDegrees is neither non-negative nor non-positive:
ArcCotDegrees has both singularity and discontinuity at zero:
ArcCotDegrees is neither convex nor concave:
ArcCotDegrees is convex for x in [0,100]:
TraditionalForm formatting:
Integration (2)
Indefinite integral of ArcCotDegrees:
Definite integral of ArcCotDegrees over an interval centered at the origin is 0:
Series Expansions (4)
Find the Taylor expansion using Series:
Plot the first three approximations for ArcCotDegrees around :
Find series expansions at branch points and branch cuts:
Asymptotic expansion at a singular point:
ArcCotDegrees can be applied to a power series:
Function Identities and Simplifications (2)
Use FullSimplify to simplify expressions with ArcCotDegrees:
Use TrigToExp to express ArcCotDegrees using Log:
Function Representations (1)
Represent using ArcTanDegrees:
Applications (8)
Solve inverse trigonometric equations:
Solve an inverse trigonometric equation with a parameter:
Use Reduce to solve inequalities involving ArcCotDegrees:
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 ArcCotDegrees:
Different combinations of ArcCotDegrees with trigonometric functions:
Addition theorem for cotangent function:
Find angles of the right triangle with sides 3, 4 and hypotenuse 5:
Properties & Relations (5)
Compositions with the inverse trigonometric functions:
Use PowerExpand to disregard multivaluedness of the ArcCotDegrees:
Alternatively, evaluate under additional assumptions:
Branch cut of ArcCotDegrees runs along the imaginary axis:
ArcCotDegrees gives the angle in degrees, while ArcCot gives the same angle in radians:
FunctionExpand applied to ArcCotDegrees 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 ArcCotDegrees:
Numerical value of this angle in degrees:
Plot ArcCotDegrees at integer points:
Text
Wolfram Research (2024), ArcCotDegrees, Wolfram Language function, https://reference.wolfram.com/language/ref/ArcCotDegrees.html.
CMS
Wolfram Language. 2024. "ArcCotDegrees." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ArcCotDegrees.html.
APA
Wolfram Language. (2024). ArcCotDegrees. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ArcCotDegrees.html