Basic Ratios
sin(θ) = opposite / hypotenuse
cos(θ) = adjacent / hypotenuse
tan(θ) = opposite / adjacent
csc(θ) = 1 / sin(θ)
sec(θ) = 1 / cos(θ)
cot(θ) = 1 / tan(θ)
Pythagorean Identities
sin²(θ) + cos²(θ) = 1
1 + tan²(θ) = sec²(θ)
1 + cot²(θ) = csc²(θ)
Sum & Difference
sin(A±B) = sinA cosB ± cosA sinB
cos(A±B) = cosA cosB ∓ sinA sinB
tan(A±B) = (tanA ± tanB) / (1 ∓ tanA tanB)
Double Angle
sin(2θ) = 2 sinθ cosθ
cos(2θ) = cos²θ - sin²θ
tan(2θ) = 2tanθ / (1 - tan²θ)
Law of Sines & Cosines
a/sin(A) = b/sin(B) = c/sin(C)
c² = a² + b² - 2ab cos(C)
Area = ½ab sin(C)