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Matematicas

Calculadora verificada con fórmula transparente

Matematicas

Double Angle Formula Calculator.

Calculates the sine, cosine, or tangent of double an angle using the double angle identities.

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Tus entradas

Cómo funciona

  1. 1

    Enter the angle in degrees.

  2. 2

    Select the trigonometric function (sin, cos, or tan).

  3. 3

    The calculator computes the double angle (2θ) and evaluates the chosen function.

  4. 4

    The result is displayed with four decimal places.

function == 'sin' ? sin(2 * angle_deg * pi / 180) : (function == 'cos' ? cos(2 * angle_deg * pi / 180) : tan(2 * angle_deg * pi / 180))

Preguntas frecuentes

What are the double angle formulas?

sin(2θ) = 2 sinθ cosθ, cos(2θ) = cos²θ - sin²θ, tan(2θ) = 2 tanθ / (1 - tan²θ).

Why is the result for cos(2*45°) exactly 0?

Because cos(90°) = 0, and 2*45° = 90°.

Can I use angles in radians?

This calculator uses degrees. Convert radians to degrees by multiplying by 180/π.

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Resultados

Fórmula verificada

Result

0,866

Pregunta lo que sea

Estimación solo como guía general: verifica decisiones importantes con un profesional adecuado.

Cómo funciona

Calculates the sine, cosine, or tangent of double an angle using the double angle identities.

  1. Enter the angle in degrees.
  2. Select the trigonometric function (sin, cos, or tan).
  3. The calculator computes the double angle (2θ) and evaluates the chosen function.
  4. The result is displayed with four decimal places.

Fórmulas

Las matemáticas detrás de esta calculadora, escritas para que puedas verificar el resultado.

Sine double angle

sin(2θ) = 2 sinθ cosθ

The sine of twice an angle equals twice the product of sine and cosine of the original angle.

Example:

Input: θ = 30°

Calculation: 2 * sin(30°) * cos(30°) = 2 * 0.5 * 0.8660

Result: ≈ 0.8660

Cosine double angle

cos(2θ) = cos²θ - sin²θ

The cosine of twice an angle equals the difference between the squares of cosine and sine.

Example:

Input: θ = 45°

Calculation: cos²(45°) - sin²(45°) = 0.5 - 0.5

Result: = 0

Casos de uso reales

Dónde aparece este cálculo en la vida cotidiana.

Simplifying trigonometric expressions

Use double angle identities to rewrite expressions in simpler forms.

Example: Rewrite sin(2x) as 2 sin x cos x.

Solving trigonometric equations

Convert double angle terms to single angles to solve equations.

Example: Solve sin(2θ) = 0.5 for θ.

Physics and engineering

Model wave interference and harmonic motion where double angles appear.

Example: Calculating the resultant amplitude of two waves.

Consejos y errores comunes

Tips

  • Remember that the double angle formula works for any angle, not just acute ones.
  • For tangent, the formula is undefined when tanθ = ±1 (i.e., θ = 45° + 90°k).
  • Use the calculator to check your manual calculations.
  • Angles can be negative; the formulas still hold.

Common Mistakes to Avoid

  • Forgetting to convert degrees to radians when using a calculator in radian mode.
  • Using the wrong sign for cosine double angle: cos(2θ) = cos²θ - sin²θ, not cos²θ + sin²θ.
  • Assuming tan(2θ) = 2 tanθ, which is incorrect.

Supuestos y limitaciones

  • Use the stated inputs and units.
  • Results are estimates for planning and education.
  • Check measurements and source data before making an important decision.