Advanced Precalculus: Trigonometry, Conics, and Complex Numbers

(Math 1060)

Kevin Wortman, copyright 2015

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Getting Started

  • Introduction
  • Proofs
  • Sets
  • Functions
  • Inverse Functions
  • Equations in One Variable I
  • Linear Algebra

  • The Plane of Vectors
  • Matrices
  • Equations in One Variable II
  • Solutions of Polynomial Equations in Two Variables

  • Polynomials in Two Variables
  • Polynomial Equations
  • Composing Polynomials with Planar Transformations
  • Linear Equations and Lines
  • Unions of Solutions
  • Quadratic Equations and Conics
  • Equations in One Variable III
  • Equations in One Variable IV
  • Measurements in the Plane

  • More about Proofs
  • Distance in the Plane
  • Circles and Pi
  • Angles
  • Ellipses and Hyperbolas
  • Equations in One Variable V
  • Trigonometry

  • Sine and Cosine
  • Tangent and Right Triangles
  • Polar Coordinates
  • Law of Sines
  • Law of Cosines
  • Rotation Matrices
  • Cosecant, Secant, and Cotangent
  • Planar Transformations of Graphs
  • Partial Inverse Trigonometric Functions
  • Trigonometric Identities
  • Equations in One Variable VI
  • Return to Conics

  • Classification of Conics
  • Equations in One Variable VII
  • Complex Numbers

  • The Plane of Complex Numbers
  • Polar Coordinates and Multiplication
  • The Cubic Formula

  • Index
  • errata
  •