Tool / solver to resolve one or more trigonometric equations, equations with unknown variables and cos, sin, tan, etc.

Trigonometric Equation Solver - dCode

Tag(s) : Symbolic Computation

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A trigonometric equation is a mathematical expression involving an equality involving trigonometric functions such as sine ($ \sin $), cosine ($ \cos $) or tangent ($ \tan $).

__Example:__ $ \cos(x) = sin(\pi) $

Hyperbolic trigonometric functions are also possible $ \cosh() $, $ \sinh() $, etc.

All angles are in radians.

Generally the resolution involves reciprocal trigonometric functions such as arc-sine ($ \arcsin $), arc-cosine ($ \arccos $) or arc-tangent ($ \arctan $).

dCode automatically solves trigonometric equations and calculates the values of the unknowns.

__Example:__ $ \sin(x) = 0 $ returns the solution $ x = 0 $ (radian)

Some equations will have an infinite number of solutions, dCode returns the general solution (modulo $ \pi $ or $ 2\pi $ or with constants $ c_i $)

Multiple trig equations with the same variables can be combined with a logical `AND` operator: `&&` or `⋀`.

Also, any new line return will be considered as a new equation (of trigonometry).

Sometimes use Euler's formula: $ \exp(i x) = \cos(x) + i \sin(x) $ or its equivalents: $ \cos(x) = \frac{\exp(i x) + \exp(-i x)}{2} $ or $ \sin(x) = \frac{\exp(i x) - \exp(-i x)}{2i} $ can lead to simplifications.

Also use the identity $ \sin^2(x) + \cos^2(x) = 1 $ if possible.

The dCode solver does not display the calculation steps because they do not reflect the steps of a human thinking but to the steps of a machine thinking (bit-by-bit binary calculation operations) far from a hand-held resolution. dCode allows you to check a result.

dCode retains ownership of the "Trigonometric Equation Solver" source code. Except explicit open source licence (indicated Creative Commons / free), the "Trigonometric Equation Solver" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Trigonometric Equation Solver" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Trigonometric Equation Solver" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!

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The copy-paste of the page "Trigonometric Equation Solver" or any of its results, is allowed (even for commercial purposes) as long as you credit dCode!

Exporting results as a .csv or .txt file is free by clicking on the *export* icon

Cite as source (bibliography):

*Trigonometric Equation Solver* on dCode.fr [online website], retrieved on 2024-09-10,

equation,trig,trigonometric,trigonometry,equality,equal,unknown,variable,cos,sin,tan

https://www.dcode.fr/trig-equation-solver

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