Precalculus · F-TF
Double-Angle and Half-Angle Identities
sin(2θ) = 2 sinθ cosθ; cos(2θ) = cos²θ − sin²θ = 2cos²θ − 1 = 1 − 2sin²θ. Half-angle: sin(θ/2) = ±√((1−cosθ)/2).
PrecalculusCommon Core HSF-TF.C.9F-TFVerified correct ✓
Worked examples
Use the half-angle identity sin(θ/2) = √((1 − cos θ)/2) to find sin(60°) from cos(120°). Round to 4 decimal places.
Answer: 0.866
Use the identity cos(2θ) = 1 − 2sin²θ to find cos(2·30°). Round to 4 decimal places.
Answer: 0.5
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