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Sistema Matemático Verificado

Trigonometry Calculator

Simplify trigonometric expressions, solve equations, and evaluate functions.

Última verificação matemática: Jan 2026

Our Trigonometry Calculator is your swiss-army knife for trig problems. Simplify complex identities, find solutions to trigonometric equations, and evaluate functions effortlessly.

✓ Simplify Identities✓ Solve Equations✓ Interactive Graphs

Enter Expression or Equation

Examples:

Graph Visualization

Result

sin⁡(x)2+cos⁡(x)2=1\sin(x)^2 + \cos(x)^2 = 1

O que é Trigonometry Calculator?

Trigonometry examines the relationship between the angles and sides of triangles. It's built on points on a circle (Sine and Cosine).

Key functions include:

  • Sine ($\sin$): Opposite / Hypotenuse
  • Cosine ($\cos$): Adjacent / Hypotenuse
  • Tangent ($\tan$): Opposite / Adjacent ($\sin/\cos$)

Fórmula

Fundamental Identities

Pythagorean
sin⁡2θ+cos⁡2θ=1\sin^2 \theta + \cos^2 \theta = 1
Quotient
tan⁡θ=sin⁡θcos⁡θ\tan \theta = \frac{\sin \theta}{\cos \theta}
Reciprocal
sec⁡θ=1cos⁡θ,csc⁡θ=1sin⁡θ\sec \theta = \frac{1}{\cos \theta}, \csc \theta = \frac{1}{\sin \theta}
Double Angle
sin⁡(2θ)=2sin⁡θcos⁡θ\sin(2\theta) = 2\sin\theta\cos\theta

Exemplo de Cálculo

Simplification Example

Simplify (sin⁡x+cos⁡x)2+(sin⁡x−cos⁡x)2(\sin x + \cos x)^2 + (\sin x - \cos x)^2

Expand both terms:

(sin⁡2+2sin⁡cos⁡+cos⁡2)+(sin⁡2−2sin⁡cos⁡+cos⁡2)(\sin^2 + 2\sin\cos + \cos^2) + (\sin^2 - 2\sin\cos + \cos^2)

Combine like terms ($2\sin\cos$ cancels out):

2sin⁡2x+2cos⁡2x=2(sin⁡2x+cos⁡2x)=2(1)=22\sin^2 x + 2\cos^2 x = 2(\sin^2 x + \cos^2 x) = 2(1) = 2

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Perguntas Frequentes

Perguntas comuns sobre esta calculadora

Why are there multiple solutions for sin(x) = 0.5?

Trigonometric functions are periodic (they repeat). $\sin(30^\circ) = 0.5$, but so is $\sin(150^\circ)$, $\sin(390^\circ)$, etc. The solutions are infinite unless a range is specified.

What is the difference between specific and general solutions?

A specific solution might be $x = 30^\circ$. A general solution accounts for all repetitions, like $x = 30^\circ + 360^\circ n$ where $n$ is an integer.