CotDegrees
CotDegrees[θ]
gives the cotangent of degrees.
Details
![](Files/CotDegrees.en/details_1.png)
- CotDegrees and other trigonometric functions are studied in high-school geometry courses and are also used in many scientific disciplines.
- The argument of CotDegrees is assumed to be in degrees.
- CotDegrees is automatically evaluated when its argument is a simple rational multiple of
; for more complicated rational multiples, FunctionExpand can sometimes be used.
- CotDegrees of angle
is the ratio of the adjacent side to the opposite side of a right triangle:
- CotDegrees is related to SinDegrees and CosDegrees by the identity
.
- For certain special arguments, CotDegrees automatically evaluates to exact values.
- CotDegrees can be evaluated to arbitrary numerical precision.
- CotDegrees automatically threads over lists.
- CotDegrees can be used with Interval, CenteredInterval and Around objects.
- Mathematical function, suitable for both symbolic and numerical manipulation.
Examples
open allclose allBasic Examples (6)
The argument is given in radians:
Calculate CotDegrees of 45 Degree for a right triangle with unit sides:
Calculate the cotangent by hand:
Solve a trigonometric equation:
Scope (46)
Numerical Evaluation (6)
The precision of the output tracks the precision of the input:
CotDegrees can take complex number inputs:
Evaluate CotDegrees 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 CotDegrees function using MatrixFunction:
Specific Values (6)
Values of CotDegrees at fixed points:
CotDegrees has exact values at rational multiples of 60 degrees:
Simple exact values are generated automatically:
More complicated cases require explicit use of FunctionExpand:
Zeros of CotDegrees:
Find one zero using Solve:
Singular points of CotDegrees:
Visualization (4)
Plot the CotDegrees function:
Plot over a subset of the complexes:
Plot the real part of CotDegrees:
Plot the imaginary part of CotDegrees:
Polar plot with CotDegrees:
Function Properties (13)
CotDegrees is a periodic function with a period of :
Check this with FunctionPeriod:
Real domain of CotDegrees:
CotDegrees achieves all real values:
CotDegrees is an odd function:
CotDegrees has the mirror property :
CotDegrees is not an analytic function:
CotDegrees is monotonic in a specific range:
CotDegrees is not injective:
CotDegrees is surjective:
CotDegrees is neither non-negative nor non-positive:
CotDegrees has both singularities and discontinuities in points multiple to 180:
CotDegrees is neither convex nor concave:
CotDegrees is convex for x in [0,90]:
TraditionalForm formatting:
Integration (3)
Compute the indefinite integrals of CotDegrees via Integrate:
Definite integral for CotDegrees over a period:
Series Expansions (3)
Find the Taylor expansion using Series:
Plot the first three approximations for CotDegrees around :
Asymptotic expansion at a singular point:
CotDegrees can be applied to power series:
Function Identities and Simplifications (5)
Double-angle formula using TrigExpand:
Recover the original expression using TrigReduce:
Convert sums to products using TrigFactor:
Convert to exponentials using TrigToExp:
Function Representations (3)
Representation through TanDegrees:
Representation through SinDegrees and CosDegrees:
Representation through SecDegrees and CscDegrees:
Applications (12)
Basic Trigonomometric Applications (2)
Given , find the CotDegrees of the angle
using the identity
:
Find the missing adjacent side length of a right triangle if the opposite side is 5 and the angle is 30 degrees:
Trigonomometric Identities (4)
Calculate the CotDegrees value of 105 degrees using the sum and difference formulas:
Compare with the result of direct calculation:
Calculate the CotDegrees value of 15 degrees using the half-angle formula :
Compare this result with directly calculated CotDegrees:
Trigonomometric Equations (2)
Trigonomometric Inequalities (2)
Advanced Applications (2)
Properties & Relations (13)
Check that 1 degree is radians:
Basic parity and periodicity properties of the cotangent function are automatically applied:
Simplify with assumptions on parameters:
Complicated expressions containing trigonometric functions do not simplify automatically:
Use FunctionExpand to express CotDegrees in terms of radicals:
Compositions with the inverse trigonometric functions:
Solve a trigonometric equation:
Numerically find a root of a transcendental equation:
Plot the function to check if the solution is correct:
The zeros of CotDegrees:
The poles of CotDegrees:
Calculate residue symbolically and numerically:
FunctionExpand applied to CotDegrees generates expressions in trigonometric functions in radians:
ExpToTrig applied to the outputs of TrigToExp will generate trigonometric functions in radians:
CotDegrees is a numeric function:
Possible Issues (1)
Text
Wolfram Research (2024), CotDegrees, Wolfram Language function, https://reference.wolfram.com/language/ref/CotDegrees.html.
CMS
Wolfram Language. 2024. "CotDegrees." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CotDegrees.html.
APA
Wolfram Language. (2024). CotDegrees. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CotDegrees.html