Free reference·Applied Mathematics and Statistics

College Mathematics

Trigonometry, analytical geometry, calculus, linear algebra and matrix theory — the math you need to use, not memorize.

The hook

The math that shows up in survey work is tools you USE, not theorems to prove. Trig, analytic geometry, basic calculus, linear algebra. Knowing when to reach for which is the skill — pure memorization isn't.

Keep these in muscle memory

Formulas to know cold

Right triangle (SOH-CAH-TOA)
sin = opp/hyp, cos = adj/hyp, tan = opp/adj
Law of cosines
c² = a² + b² − 2ab·cos(C)
Solves any triangle when 2 sides + included angle, or all 3 sides, are known.
Law of sines
a/sin(A) = b/sin(B) = c/sin(C)
When 2 angles + 1 side, or 2 sides + non-included angle, are known.
Distance between points
d = √((x₂−x₁)² + (y₂−y₁)²)
Slope of a line
m = (y₂−y₁) / (x₂−x₁)
Quadratic formula
x = (−b ± √(b² − 4ac)) / (2a)
Memorize these

Concepts that show up on the exam

Radians vs. degrees
1 radian = 180/π degrees ≈ 57.296°. Trig functions in math libraries take radians; surveyors think in degrees. Convert with care.
Vector
Magnitude + direction. Add by components: (a₁ + b₁, a₂ + b₂). Survey lat/dep are vector components.
Matrix multiplication
Used in coordinate transformations, least squares. (m × n)(n × p) = (m × p). Inner dimensions must match.
Derivative
Instantaneous rate of change. d/dx of x² = 2x. Used in error propagation: σ_y depends on (∂y/∂xᵢ).
Integral
Cumulative sum / area under a curve. Used in volume by integration of cross-section areas, area under irregular curves (Simpson's rule).
Test yourself

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