Double Angle Formula Calculator
Calculate sin(2θ), cos(2θ), and tan(2θ) using the double angle formulas.
Enter any angle in degrees or radians and see all three results instantly.
The double angle identities express trig functions of 2θ in terms of trig functions of θ alone. They show up constantly in calculus, signal processing, and physics — anywhere you need to simplify an expression involving a doubled angle.
sin(2θ) = 2 sin(θ) cos(θ) cos(2θ) = cos²(θ) − sin²(θ) = 2cos²(θ) − 1 = 1 − 2sin²(θ) tan(2θ) = 2tan(θ) / (1 − tan²(θ))
The cosine formula has three equivalent forms. Which one you use depends on what you are already working with. If you only know sin(θ), use 1 − 2sin²(θ). If you only know cos(θ), use 2cos²(θ) − 1. The third form, cos²(θ) − sin²(θ), is the starting point for deriving the other two.
Tan(2θ) is undefined when 1 − tan²(θ) = 0, which happens at θ = 45° and θ = 135° (and their equivalents). The calculator will show “undefined” there.
Where these come up in practice: solving trig equations (rewriting 2θ terms so everything is in terms of θ), computing power-reduction formulas in integration, designing oscillator circuits where frequencies double, and in Fourier analysis where harmonics at twice the fundamental frequency appear naturally.
The chart below shows how sin(2θ) and cos(2θ) behave over a full cycle. Notice both complete two full oscillations over 0° to 360° — confirming the “double angle” name.