ArcTanDegrees
gives the arc tangent in degrees of the complex number .
Details
![](Files/ArcTanDegrees.en/details_1.png)
- ArcTanDegrees, 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
.
- ArcTanDegrees[z] returns the angle
in degrees for which the ratio of the opposite side to the adjacent side of a right triangle is
.
- For certain special arguments, ArcTanDegrees automatically evaluates to exact values.
- ArcTanDegrees can be evaluated to arbitrary numerical precision.
- ArcTanDegrees automatically threads over lists.
- ArcTanDegrees[z] has branch cut discontinuities in the complex
plane running from
to
and
to
.
- ArcTanDegrees 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 ArcTanDegrees to the following list:
Scope (40)
Numerical Evaluation (6)
The precision of the output tracks the precision of the input:
Evaluate for complex arguments:
Evaluate ArcTanDegrees 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 ArcTanDegrees function using MatrixFunction:
Specific Values (5)
Values of ArcTanDegrees at fixed points:
Simple exact values are generated automatically:
Zero of ArcTanDegrees:
Visualization (4)
Plot the ArcTanDegrees function:
Plot over a subset of the complexes:
Plot the real part of ArcTanDegrees:
Plot the imaginary part of ArcTanDegrees:
Polar plot with ArcTanDegrees:
Function Properties (12)
ArcTanDegrees is defined for all real values:
ArcTanDegrees achieves all real values from the interval :
ArcTanDegrees is an odd function:
ArcTanDegrees has the mirror property :
ArcTanDegrees is an analytic function of over the reals:
It is neither analytic nor meromorphic over the complex plane:
ArcTanDegrees is an increasing function:
ArcTanDegrees is injective:
ArcTanDegrees is not surjective:
ArcTanDegrees is neither non-negative nor non-positive:
ArcTanDegrees has no singularities or discontinuities:
ArcTanDegrees is neither convex nor concave:
ArcSind is convex for x in [-10,0]:
TraditionalForm formatting:
Integration (2)
Indefinite integral of ArcTanDegrees:
Definite integral of ArcTanDegrees over an interval centered at the origin is 0:
Series Expansions (5)
Taylor expansion for ArcTanDegrees:
Plot the first three approximations for ArcTanDegrees around :
Asymptotic expansions at Infinity:
Asymptotic expansion at one of the singular points:
Find series expansions at branch points and branch cuts:
ArcTanDegrees can be applied to a power series:
Function Identities and Simplifications (2)
Use FullSimplify to simplify expressions with ArcTanDegrees:
Use TrigToExp to express ArcTanDegrees using Log:
Function Representations (1)
Represent using ArcCotDegrees:
Applications (7)
Solve inverse trigonometric equations:
Solve an inverse trigonometric equation with a parameter:
Use Reduce to solve inequalities involving ArcTanDegrees:
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 ArcTanDegrees:
Different combinations of ArcTanDegrees with trigonometric functions:
Properties & Relations (5)
Compositions with the inverse trigonometric functions:
Use PowerExpand to disregard multivaluedness of the ArcTanDegrees:
Alternatively, evaluate under additional assumptions:
Branch cuts of ArcTanDegrees run along the imaginary axis:
ArcTanDegrees gives the angle in degrees, while ArcTan gives the same angle in radians:
FunctionExpand applied to ArcTanDegrees 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 ArcTanDegrees:
Numerical value of this angle in degrees:
Plot ArcTanDegrees at integer points:
Text
Wolfram Research (2024), ArcTanDegrees, Wolfram Language function, https://reference.wolfram.com/language/ref/ArcTanDegrees.html.
CMS
Wolfram Language. 2024. "ArcTanDegrees." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ArcTanDegrees.html.
APA
Wolfram Language. (2024). ArcTanDegrees. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ArcTanDegrees.html