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Trigonometric Equation Solver

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

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Trigonometric Equation Solver -

Tag(s) : Symbolic Computation

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Trigonometric Equation Solver

Trig Equation Solving











Answers to Questions (FAQ)

What is a trigonometric equation? (Definition)

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.

How to solve a trigonometric equation?

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 $)

How to solve multiple trigonometric equations?

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).

How to solve a trigonometric equation with Euler's formula?

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.

How to solve a trig equation step by step?

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.

Source code

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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Trigonometric Equation Solver on dCode.fr [online website], retrieved on 2024-06-16, https://www.dcode.fr/trig-equation-solver

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