ArcCosDegrees
gives the arc cosine in degrees of the complex number .
Details
![](Files/ArcCosDegrees.en/details_1.png)
- ArcCosDegrees, 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
between
and
, the results are always in the range
to
.
- ArcCosDegrees[z] returns the angle
in degrees for which the ratio of the adjacent side to the hypotenuse of a right triangle is
.
- For certain special arguments, ArcCosDegrees automatically evaluates to exact values.
- ArcCosDegrees can be evaluated to arbitrary numerical precision.
- ArcCosDegrees automatically threads over lists.
- ArcCosDegrees[z] has branch cut discontinuities in the complex
plane running from
to
and
to
.
- ArcCosDegrees 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 ArcCosDegrees to the following list:
Scope (38)
Numerical Evaluation (6)
The precision of the output tracks the precision of the input:
Evaluate for complex arguments:
Evaluate ArcCosDegrees 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 ArcCosDegrees function using MatrixFunction:
Specific Values (5)
Values of ArcCosDegrees at fixed points:
Simple exact values are generated automatically:
Zero of ArcCosDegrees:
Visualization (4)
Plot the ArcCosDegrees function:
Plot over a subset of the complexes:
Plot the real part of ArcCosDegrees:
Plot the imaginary part of ArcCosDegrees:
Polar plot with ArcCosDegrees:
Function Properties (10)
ArcCosDegrees is defined for all real values from the interval :
Complex domain is the whole plane:
ArcCosDegrees achieves all real values from the interval :
ArcCosDegrees is not an analytic function:
ArcCosDegrees is neither non-decreasing nor non-increasing:
It is monotonic over its real domain:
ArcCosDegrees is injective:
ArcCosDegrees is not surjective:
ArcCosDegrees is non-negative over its real domain:
ArcCosDegrees has both singularity and discontinuity in (-∞,-1] and [1,∞):
ArcCosDegrees is neither convex nor concave:
ArcCosDegrees is convex for x in [-1,0]:
TraditionalForm formatting:
Integration (2)
Indefinite integral of ArcCosDegrees:
Definite integral of ArcCosDegrees over the entire real domain:
Series Expansions (5)
Find the Taylor expansion using Series:
Plot the first three approximations for ArcCosDegrees around :
Asymptotic expansion at Infinity:
Asymptotic expansion at a singular point:
Find the series expansion at branch points and branch cuts:
ArcCosDegrees can be applied to power series:
Function Identities and Simplifications (2)
Simplify expressions involving ArcCosDegrees:
Use TrigToExp to express through logarithms and square roots:
Function Representations (1)
Represent using ArcSecDegrees:
Applications (8)
Solve an inverse trigonometric equation:
Solve an inverse trigonometric equation with a parameter:
Get the zeros of ArcCosDegrees:
Use Reduce to solve inequalities involving ArcCosDegrees:
Numerically find a root of a transcendental equation:
Plot the function to check if the solution is correct:
Plot the real and imaginary part of ArcCosDegrees:
Plot the Riemann surface of ArcCosDegrees:
Properties & Relations (5)
Compose with the inverse function:
Use PowerExpand to disregard multivaluedness of the ArcCosDegrees:
Alternatively, evaluate under additional assumptions:
This shows the branch cuts of the ArcCosDegrees function:
ArcCosDegrees gives the angle in degrees, while ArcCos gives the same angle in radians:
FunctionExpand applied to ArcCosDegrees generates expressions in trigonometric functions in radians:
ExpToTrig applied to the outputs of TrigToExp will generate trigonometric functions in radians:
Possible Issues (3)
Neat Examples (3)
Solve trigonometric equations involving ArcCosDegrees:
Numerical value of this angle in degrees:
Plot a specific ArcCosDegrees:
Plot ArcCosDegrees at integer points:
Text
Wolfram Research (2024), ArcCosDegrees, Wolfram Language function, https://reference.wolfram.com/language/ref/ArcCosDegrees.html.
CMS
Wolfram Language. 2024. "ArcCosDegrees." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ArcCosDegrees.html.
APA
Wolfram Language. (2024). ArcCosDegrees. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ArcCosDegrees.html