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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

 Solving Domain Set R (Reals) Z (Integers) C (Complex)
 Result Format Automatic Selection Exact Value (when possible) Approximate Numerical Value Scientific Notation

### 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.

### 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.

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Trigonometric Equation Solver on dCode.fr [online website], retrieved on 2024-09-10, https://www.dcode.fr/trig-equation-solver

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