sin(2θ) Calculator — Double Angle Formula for Sine
Enter angle θ in degrees or radians to compute sin(2θ) using the double-angle identity 2 sin θ cos θ, along with cos(2θ) and tan(2θ).
°
Angle unit
Double-angle sine — always in [−1, 1]
- 1
Convert to radians
30 × π ÷ 180 = 0.523599 - 2
sin(θ)
sin(0.523599) = 0.5 - 3
cos(θ)
cos(0.523599) = 0.866025 - 4
Apply double-angle identity
2 × 0.5 × 0.866025 = 0.866025
How does this calculator work?
sin(2θ) = 2 sin θ cos θ. Plug in any angle θ (degrees or radians) to get the doubled-angle sine and its companions cos(2θ) and tan(2θ). sin(2θ) is always in [−1, 1], peaks at θ = 45°, and has twice the frequency of sin(θ).
Formula
How this is calculated
The double-angle identity for sine derives from the angle-addition formula sin(A + B) = sin A cos B + cos A sin B. Setting A = B = θ gives sin(2θ) = sin θ cos θ + cos θ sin θ = 2 sin θ cos θ. This identity is fundamental in calculus for integrating products of sin and cos, in signal processing for frequency doubling, and in solving trigonometric equations where a single-angle form is needed.
The result is computed directly as 2 sin θ cos θ and cross-checked via Math.sin(2θ); any tiny floating-point discrepancy is below 1 × 10⁻¹⁴. The companion values cos(2θ) and tan(2θ) follow from the same 2θ. tan(2θ) is undefined wherever cos(2θ) = 0 — that is, when θ = 45°, 135°, 225°, 315°, and so on.
Note that sin(2θ) oscillates at twice the frequency of sin(θ): while sin(θ) has a period of 360°, sin(2θ) completes a full cycle every 180°. Like all sine values it always stays in [−1, 1], reaching its maximum of 1 at θ = 45° and minimum of −1 at θ = 135°.
Frequently asked questions
sin(2θ) = 2 sin θ cos θ. This double-angle identity comes directly from the sine addition formula applied to θ + θ. It expresses the sine of the doubled angle entirely in terms of the original angle's sine and cosine.
sin(2θ) = 0 when 2θ = 0°, 180°, 360°, …, i.e. when θ = 0°, 90°, 180°, 270°. At those angles either sin θ or cos θ is zero, making their product zero.
tan(2θ) is undefined when cos(2θ) = 0, which happens at θ = 45°, 135°, 225°, 315°. The calculator displays "undefined" at those points.
TG we-Calculate Editorial Team. (2026). sin(2θ) Calculator — Double Angle Formula for Sine [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/sin-2-theta-calculator
TG we-Calculate Editorial Team. "sin(2θ) Calculator — Double Angle Formula for Sine." TG we-Calculate. 2026. https://we-calculate.com/calculator/sin-2-theta-calculator.
TG we-Calculate Editorial Team, "sin(2θ) Calculator — Double Angle Formula for Sine," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/sin-2-theta-calculator
@misc{wecalculate_sin_2_theta_calculator, title = {sin(2θ) Calculator — Double Angle Formula for Sine}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/sin-2-theta-calculator}}, year = {2026}, note = {TG we-Calculate} }
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