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