Geometry & Trigonometry — Cheat Sheet
Areas, volumes, triangle solving and the trig identities you keep forgetting.
Law of cosines: c² = a² + b² − 2ab·cos C; law of sines: a/sin A = b/sin B = c/sin C.
Areas
| Rectangle | A = b·h |
| Triangle | A = ½·b·h |
| Circle | A = πr² = πd²/4 |
| Ellipse | A = π·a·b |
| Trapezoid | A = ½(a+b)·h |
| Regular hexagon | A = (3√3/2)s² |
Volumes & surface
| Cylinder | V = πr²h, A = 2πr(r+h) |
| Sphere | V = 4/3·πr³, A = 4πr² |
| Cone | V = ⅓·πr²h |
| Box | V = l·w·h |
Right triangle
| Pythagoras | c² = a² + b² |
| sin | opposite / hypotenuse |
| cos | adjacent / hypotenuse |
| tan | opposite / adjacent |
Any triangle
| Law of cosines | c² = a² + b² − 2ab·cos C |
| Law of sines | a/sinA = b/sinB = c/sinC |
| Area (SAS) | A = ½·a·b·sin C |
| Angle sum | A + B + C = 180° |
Identities
| Pythagorean | sin²θ + cos²θ = 1 |
| Double angle | sin2θ = 2sinθcosθ |
| Tangent | tanθ = sinθ / cosθ |
| Arc length | s = r·θ (θ in rad) |
Formula reference — verify against the governing standard. Not a substitute for engineering judgment.