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Geometry & Trigonometry

Chapter 1 · Right Triangles & Beyond

📋 Reference · always available
SOH–CAH–TOA
sin⁡θ=opphyp,    cos⁡θ=adjhyp,    tan⁡θ=oppadj\sin\theta = \tfrac{\text{opp}}{\text{hyp}},\;\; \cos\theta = \tfrac{\text{adj}}{\text{hyp}},\;\; \tan\theta = \tfrac{\text{opp}}{\text{adj}}
Pythagoras
a2+b2=c2a^2 + b^2 = c^2
Sine rule
asin⁡A=bsin⁡B=csin⁡C\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
Cosine rule
c2=a2+b2−2abcos⁡Cc^2 = a^2 + b^2 - 2ab\cos C
Triangle area
Area=12absin⁡C\text{Area} = \tfrac{1}{2}ab\sin C
SOH-CAH-TOA
sin⁡=oh,cos⁡=ah,tan⁡=oa\sin=\tfrac{o}{h},\cos=\tfrac{a}{h},\tan=\tfrac{o}{a}
Sine / cosine rule
asin⁡A=bsin⁡B,    a2=b2+c2−2bccos⁡A\tfrac{a}{\sin A}=\tfrac{b}{\sin B},\;\; a^2=b^2+c^2-2bc\cos A
Area & arc/sector
Area=12absin⁡C,    s=rθ,  A=12r2θ\text{Area}=\tfrac12 ab\sin C,\;\; s=r\theta,\; A=\tfrac12 r^2\theta
Common trap
Arc/sector formulas need θ in RADIANS; sine rule has an ambiguous (two-angle) case.