数学
已验证计算器，公式透明
Double Angle Formula Calculator.
Calculates the sine, cosine, or tangent of double an angle using the double angle identities.
您的输入
工作原理
- 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))常见问题
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.
工作原理
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.
公式
此计算器背后的数学公式，供您核对结果。
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
实际应用场景
此计算在日常生活中的应用。
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.
提示与常见错误
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.
假设与限制
- Use the stated inputs and units.
- Results are estimates for planning and education.
- Check measurements and source data before making an important decision.