Double Angle Formula Calculator

Work out double angle formula instantly with clear inputs, formula shown and shareable results.

About Double Angle Formula Calculator

The double-angle formulas come from the sum formulas with both angles equal: sin 2θ = 2 sin θ cos θ, cos 2θ = cos²θ − sin²θ = 1 − 2sin²θ = 2cos²θ − 1, and tan 2θ = 2 tan θ / (1 − tan²θ).

Formulas

Sine

sin 2θ = 2 sin θ cos θ

Cosine

cos 2θ = cos²θ − sin²θ = 1 − 2sin²θ

Tangent

tan 2θ = 2 tan θ / (1 − tan²θ)

Worked example

With the default values below, Double Angle Formula Calculator returns sin 2θ of 0.86602540. Change any input above and every figure here is recalculated in your browser.

Inputs used

Angle θ: 30
Angle unitone of Degrees, Radians, Gradians: Degrees

Results

sin 2θ: 0.86602540
cos 2θ: 0.50000000
tan 2θ (0 at the asymptote): 1.73205081
cos 2θ via 1 − 2sin²θ: 0.50000000

Step by step

1Values used
2Sine
3Cosine
4Tangent
5sin 2θ= 0.86602540
6cos 2θ= 0.50000000
7tan 2θ (0 at the asymptote)= 1.73205081
8cos 2θ via 1 − 2sin²θ= 0.50000000

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For θ = 30°?

sin 60° = 0.8660254, cos 60° = 0.5 and tan 60° = 1.7320508.

When is tan 2θ undefined?

When 2θ is an odd multiple of 90°, for example θ = 45°. The calculator reports 0 there rather than infinity.