ConceptGeometry & Algebra

Key formulas

Degree-radian: radians = degrees × π/180
Pythagorean identity: sin² x + cos² x = 1; tan x = sin x / cos x
Periods: 2π for sin and cos, π for tan
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 2x = 2 sin x cos x; cos 2x = cos² x − sin² x = 2cos² x − 1 = 1 − 2sin² x
Half-angle and product-to-sum / sum-to-product formulas (standard set)
Triangle angle sum: A + B + C = π (so C = π − (A+B))
Sine Rule: a/sin A = b/sin B = c/sin C = 2R
Law of Cosines: c² = a² + b² − 2ab cos C
Triangle area: S = (1/2)ab sin C
y = A sin(ωx + φ): amplitude A, period 2π/ω; horizontal stretch by factor k uses ω → ω/k

If the concept underneath still feels loose, patch it here before returning to CSCA questions.

FoundationsPrecalculus bridge Algebra 2 foundations

Ellipse: definition (sum of focal distances=2a), standard equation, a²=b²+c², focal-triangle area with angle condition

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Ellipse: definition (sum of focal distances=2a), standard equation, a2=b2+c2, focal-triangle area with angle condition

Ellipse: definition (sum of focal distances=2a), standard equation, a²=b²+c², focal-triangle area with angle condition