Double Angle Calculator — sin(2θ), cos(2θ), tan(2θ)
Enter any angle θ in degrees or radians to instantly compute sin(2θ), cos(2θ) and tan(2θ) using the standard double-angle trigonometric identities.
Angle unit
sin(2θ) = 2 · sin θ · cos θ
- 1
Convert to radians
30 × π ÷ 180 = 0.523599 - 2
sin θ and cos θ
sin θ = 0.5, cos θ = 0.866025 - 3
Apply double-angle formula
2 × 0.5 × 0.866025 = 0.866025sin(2θ) = 2 sin θ cos θ
How does this calculator work?
The double-angle formulas give sin(2θ) = 2 sin θ cos θ, cos(2θ) = cos²θ − sin²θ, and tan(2θ) = 2 tan θ / (1 − tan²θ). Enter an angle in degrees or radians to compute all three at once. Tan(2θ) is undefined when tan²θ = 1 (at 45° and equivalents).
Formula
How this is calculated
The double-angle identities express trigonometric functions of twice an angle in terms of the functions of the original angle. Starting from the angle addition formulas — sin(A + B) = sin A cos B + cos A sin B and cos(A + B) = cos A cos B − sin A sin B — setting A = B = θ yields sin(2θ) = 2 sin θ cos θ and cos(2θ) = cos²θ − sin²θ. Dividing the sine form by the cosine form gives tan(2θ) = 2 tan θ / (1 − tan²θ).
This calculator converts degree inputs to radians (multiplying by π/180) before evaluating the built-in sin and cos functions, then applies the identities. Tan(2θ) is marked undefined when cos(2θ) = 0 (i.e., when 2θ is an odd multiple of 90°) or equivalently when tan²θ = 1 (θ at 45°, 135°, etc.).
The results are numerically precise to floating-point accuracy. Note that for special angles (0°, 30°, 45°, 60°, 90°) you may see tiny rounding residuals (e.g. 6.12e-17 instead of exactly 0) because of how IEEE 754 binary arithmetic works; round those to zero if an exact symbolic result is needed.
Frequently asked questions
sin(2θ) = 2 sin θ cos θ. It follows directly from the sine addition formula sin(A + B) = sin A cos B + cos A sin B with A = B = θ.
tan(2θ) = 2 tan θ / (1 − tan²θ). The denominator is zero when tan²θ = 1, i.e., when θ = 45°, 135°, 225°, or 315°. At those angles the tangent of the double angle is undefined.
Yes. Switch the unit selector to radians and enter the value directly, for example π/6 ≈ 0.5236 for 30°.
TG we-Calculate Editorial Team. (2026). Double Angle Calculator — sin(2θ), cos(2θ), tan(2θ) [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/double-angle-calculator
TG we-Calculate Editorial Team. "Double Angle Calculator — sin(2θ), cos(2θ), tan(2θ)." TG we-Calculate. 2026. https://we-calculate.com/calculator/double-angle-calculator.
TG we-Calculate Editorial Team, "Double Angle Calculator — sin(2θ), cos(2θ), tan(2θ)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/double-angle-calculator
@misc{wecalculate_double_angle_calculator, title = {Double Angle Calculator — sin(2θ), cos(2θ), tan(2θ)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/double-angle-calculator}}, year = {2026}, note = {TG we-Calculate} }
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