Double Angle Formula Calculator
Calculate trigonometric functions of double angles using various formulas.
Double Angle Formulas
The double angle formulas are:
- \[ \sin(2\theta) = 2\sin(\theta)\cos(\theta) \]
- \[ \cos(2\theta) = \cos^2(\theta) - \sin^2(\theta) = 2\cos^2(\theta) - 1 = 1 - 2\sin^2(\theta) \]
- \[ \tan(2\theta) = \frac{2\tan(\theta)}{1 - \tan^2(\theta)} \]
Properties:
- These formulas express trigonometric functions of double angles in terms of single angles
- Useful for simplifying expressions and solving equations
- Important in calculus and physics
- Can be derived from sum formulas
Applications:
- Trigonometry
- Calculus (integration)
- Physics (wave motion)
- Engineering (signal processing)
- Computer graphics
Common Values:
- \(\sin(2 \cdot 0) = 0\)
- \(\sin(2 \cdot \frac{\pi}{4}) = 1\)
- \(\cos(2 \cdot 0) = 1\)
- \(\cos(2 \cdot \frac{\pi}{4}) = 0\)
- \(\tan(2 \cdot 0) = 0\)
- \(\tan(2 \cdot \frac{\pi}{8}) = 1\)