Geometry & Trigonometry

Right Triangle Trigonometry

SOH-CAH-TOA:

• sin θ = opposite/hypotenuse
• cos θ = adjacent/hypotenuse
• tan θ = opposite/adjacent

Special triangles: 30-60-90 (sides 1:√3:2) and 45-45-90 (sides 1:1:√2).

Circles

• Standard equation: (x−h)² + (y−k)² = r² → centre (h,k), radius r
• Inscribed angle = half the central angle subtending the same arc
• Tangent-radius angle is always 90°

Coordinate Geometry

• Line through two points: find slope m, then use y−y₁ = m(x−x₁)
• Perpendicular lines: slopes are negative reciprocals (m₁ × m₂ = −1)
• Area with coordinates: Shoelace formula for polygons with known vertices