Compute sin(2θ), cos(2θ) — with all three equivalent forms — and tan(2θ) from any angle θ. See the step-by-step substitution and unit circle showing both θ and 2θ.
sin(2θ) = 2 sin θ cos θ
cos(2θ) = cos²θ − sin²θ = 2cos²θ − 1 = 1 − 2sin²θ
tan(2θ) = 2 tan θ / (1 − tan²θ)
The double angle formulas follow from the sum formulas: sin(2θ) = sin(θ+θ) and cos(2θ) = cos(θ+θ). The three forms of cos(2θ) come from substituting the Pythagorean identity sin²θ + cos²θ = 1.
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