Математика
Проверенный калькулятор с прозрачной формулой
Double Angle Formula Calculator.
Calculates the sine, cosine, or tangent of double an angle using the double angle identities.
Ваши данные
Как это работает
- 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.
function == 'sin' ? sin(2 * angle_deg * pi / 180) : (function == 'cos' ? cos(2 * angle_deg * pi / 180) : tan(2 * angle_deg * pi / 180))Часто задаваемые вопросы
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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Результаты
Формула проверенаResult
0,866
Оценка только для общего руководства — проверяйте важные решения с соответствующим специалистом.
Как это работает
Calculates the sine, cosine, or tangent of double an angle using the double angle identities.
- Enter the angle in degrees.
- Select the trigonometric function (sin, cos, or tan).
- The calculator computes the double angle (2θ) and evaluates the chosen function.
- The result is displayed with four decimal places.
Формулы
Математика, лежащая в основе этого калькулятора, изложена так, чтобы вы могли проверить результат.
Sine double angle
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
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
Примеры из реальной жизни
Где этот расчет встречается в повседневной жизни.
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.
Советы и частые ошибки
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.
Допущения и ограничения
- Use the stated inputs and units.
- Results are estimates for planning and education.
- Check measurements and source data before making an important decision.