Sin(2θ) Double Angle Calculator

Calculate sin(2θ) using the double angle formula: sin(2θ) = 2 · sin(θ) · cos(θ).

Enter Angle θ

Result

sin(2 × 30°)
0.866025
sin(θ)0.5
cos(θ)0.866025
2 · sin(θ) · cos(θ)0.866025
2θ in Degrees60°
2θ in Radians1.047198 rad
cos(2θ)0.5
tan(2θ)1.732051

Step-by-Step Solution

sin(2θ) = 2 · sin(θ) · cos(θ)

The Double Angle Formula for Sine

The double angle formula for sine states that sin(2θ) = 2 · sin(θ) · cos(θ). This identity allows you to compute the sine of twice an angle using only the sine and cosine of the original angle, without needing to know the doubled angle directly.

All Double Angle Formulas

sin(2θ)

Double angle formula for sine.

sin(2θ) = 2 sin(θ) cos(θ)

cos(2θ)

Double angle formula for cosine (three equivalent forms).

cos(2θ) = cos²(θ) - sin²(θ)

tan(2θ)

Double angle formula for tangent.

tan(2θ) = 2tan(θ) / (1 - tan²(θ))

Derivation

The double angle formula can be derived from the angle addition formula: sin(A + B) = sin(A)cos(B) + cos(A)sin(B). Setting A = B = θ:

sin(θ + θ) = sin(θ)cos(θ) + cos(θ)sin(θ) = 2sin(θ)cos(θ)

Applications

  • Simplifying trigonometric expressions in calculus.
  • Solving trigonometric equations.
  • Signal processing and Fourier analysis.
  • Physics: projectile motion (range formula uses sin(2θ)).
  • Computing areas and arc lengths in geometry.