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Advanced Precalculus

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

• The Plane of Vectors
• Matrices
• Equations in One Variable II

• 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

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

• Sine and Cosine
• Tangent and Right Angles
• Polar Coordinates
• Law of Sines
• Law of Cosines
• Rotation Matrix
• Cosecant, Secant, and Cotangent
• Planar Transformations of Graphs
• Partial Inverse Trigonometric Functions
• Equations in One Variable VI

• Classification of Conics
• Equations in One Variable VII

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

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