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Concept · Geometry & Algebra
Solving triangles
Sine Rule, Law of Cosines, area=(1/2)ab sinC; angle from a parallel-vector/collinearity condition
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Key formulas
11- Degree-radianradians = degrees × π/180
- Pythagorean identitysin2 x + cos2 x = 1tan x = sin x / cos x
- Periods2π for sin and cos, π for tan
- Sum/differencesin(A±B)=sinA cosB ± cosA sinBcos(A±B)=cosA cosB ∓ sinA sinBtan(A±B)=(tanA ± tanB)/(1 ∓ tanA tanB)
- Double-anglesin 2x = 2 sin x cos xcos 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 sumA + B + C = π (so C = π − (A+B))
- Sine Rulea/sin A = b/sin B = c/sin C = 2R
- Law of Cosinesc2 = a2 + b2 − 2ab cos C
- Triangle areaS = (1/2)ab sin C
- y = A sin(ωx + φ): amplitude A, period 2π/ωhorizontal stretch by factor k uses ω → ω/k
Shaky underneath?
If the concept underneath still feels loose, patch it here before coming back to CSCA questions.
FoundationsPrecalculus bridgeAlgebra 2 foundations