Double Angle Formula Calculator

Formulas

The double angle formulas are:

\(\sin(2\theta) = 2 \sin(\theta) \cos(\theta)\)
\(\cos(2\theta) = \cos^2(\theta) - \sin^2(\theta)\)
\(\tan(2\theta) = \frac{2 \tan(\theta)}{1 - \tan^2(\theta)}\)

Example

Let's say the angle is 30°. Using the formulas:

\(\sin(2 \times 30°) = 2 \sin(30°) \cos(30°) = 2 \times 0.5 \times 0.866 = 0.866\)
\(\cos(2 \times 30°) = \cos^2(30°) - \sin^2(30°) = 0.866^2 - 0.5^2 = 0.5\)
\(\tan(2 \times 30°) = \frac{2 \tan(30°)}{1 - \tan^2(30°)} = \frac{2 \times 0.577}{1 - 0.577^2} = 1.732\)

What are Double Angle Formulas?

Double angle formulas are trigonometric identities that express trigonometric functions of double angles (2θ) in terms of functions of the original angle (θ). They are useful in simplifying and solving trigonometric equations.