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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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
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Cite as source (bibliography):
Trigonometric Equation Solver on dCode.fr [online website], retrieved on 2024-11-21,
