Trigonometry Identities and Formulas

Flashcards covering sum & difference identities, double and half angle identities, laws of sines and cosines, area of a triangle, arc length, sector area, and linear/angular velocity.

Sum Identity for sin(A+B)

sin(A + B) = sin A cos B + cos A sin B

Difference Identity for sin(A-B)

sin(A - B) = sin A cos B - cos A sin B

Sum Identity for cos(A+B)

cos(A + B) = cos A cos B - sin A sin B

Difference Identity for cos(A-B)

cos(A - B) = cos A cos B + sin A sin B

Sum Identity for tan(A+B)

tan(A + B) = (tan A + tan B) / (1 - tan A tan B)

Difference Identity for tan(A-B)

tan(A - B) = (tan A - tan B) / (1 + tan A tan B)

Double Angle Identity for sin(2θ)

sin(2θ) = 2sinθ cosθ

Double Angle Identity for cos(2θ)

cos(2θ) = cos²θ - sin²θ = 2cos²θ - 1 = 1 - 2sin²θ

Double Angle Identity for tan(2θ)

tan(2θ) = (2tanθ) / (1 - tan²θ)

Half Angle Identity for cos(θ/2)

cos(θ/2) = ±√((1 + cosθ) / 2)

Half Angle Identity for sin(θ/2)

sin(θ/2) = ±√((1 - cosθ) / 2)

Half Angle Identity for tan(θ/2)

tan(θ/2) = (1 - cosθ) / sinθ = sinθ / (1 + cosθ) = ±√((1 - cosθ) / (1 + cosθ))

Angular Velocity

ω = θ/t