Compute sin(2θ), cos(2θ), and tan(2θ) using double-angle identities from an input angle in degrees or radians.
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Trigonometry
The double-angle calculator applies the double-angle formulas to compute sin(2θ), cos(2θ), and tan(2θ) from an input angle in degrees or radians.
The three main double-angle identities are: sin(2θ) = 2 sin(θ) cos(θ), cos(2θ) = cos²(θ) - sin²(θ), and tan(2θ) = 2 tan(θ) / (1 - tan²(θ)).
The cosine double-angle formula has two equivalent forms: cos(2θ) = 2cos²(θ) - 1 = 1 - 2sin²(θ). These are useful for integration and simplifying expressions.
Double-angle formulas simplify expressions in calculus (especially integration of trigonometric functions), physics (wave interference, signal processing), and geometry (inscribed angle problems).
Frequently asked questions
sin(60°) = sqrt(3)/2 ≈ 0.866. Using the formula: 2 sin(30°) cos(30°) = 2 × 0.5 × sqrt(3)/2 = sqrt(3)/2.
When 1 - tan²(θ) = 0, i.e. when tan(θ) = ±1 (at 45°, 135°, etc.). At these angles, 2θ = 90° or 270° where tangent itself is undefined.
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