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Mathematics

Geometry and Trigonometry

Key Points

  • Sum of angles in a triangle = 180°
  • Sum of angles in a quadrilateral = 360°
  • Pythagoras theorem: a² + b² = c² (right-angled triangle)
  • SOHCAHTOA: Sin=Opp/Hyp, Cos=Adj/Hyp, Tan=Opp/Adj
  • Circle theorems: angle in semicircle = 90°, angles in same segment are equal

Detailed Notes

Geometry and Trigonometry covers shapes, angles, and trigonometric ratios. For triangles, know the sine rule and cosine rule. For circles, master all circle theorems. For coordinate geometry, know the distance formula, midpoint formula, and equation of a straight line. Trigonometry: memorise SOHCAHTOA and the special angles (30°, 45°, 60°).

Key Formulas & Facts

Pythagoras Theorem
a² + b² = c²
Area of Triangle
A = ½ × base × height
Sine Rule
a/sinA = b/sinB = c/sinC
Cosine Rule
a² = b² + c² - 2bc·cosA
SOHCAHTOA
sin θ = Opp/Hyp; cos θ = Adj/Hyp; tan θ = Opp/Adj
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