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Precalculus Algebra and Trigonometry: Syllabus, Competencies, and Course Structure

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Understanding Polynomial Functions

Graphing Polynomial Functions

Introduction to Rational Functions

Asymptotes

Graphing Rational Functions

Exponents

Introduction to Exponential Functions

Graphing Exponential Functions

Introduction to Logarithms

Graphing Logarithmic Functions

Properties of Logarithms

Solving Exponential and Logarithmic Equations

Trigonometric Functions on Right Triangles

Defining the Unit Circle

Trigonometric Functions on the Unit Circle

Graphs of the Sine and Cosine Functions

Graphs of Tangent and Cotangent Functions

Inverse Sine, Cosine, & Tangent

Linear Trigonometric Equations

Introduction to Trigonometric Identities

Sum and Difference Identities

Double Angle Identities

Solving Trigonometric Equations Using Identities

Law of Sines

Law of Cosines

Polar Coordinate System

Graphing Complex Numbers

Polar Form of Complex Numbers

Powers of Complex Numbers (DeMoivre's Theorem)

Introduction to Conic Sections

Parabolas

Ellipses: Standard Form

Hyperbolas at the Origin

Hyperbolas NOT at the Origin

Two Variable Systems of Linear Equations

Introduction to Matrices

Determinants and Cramer's Rule

Sequences

Arithmetic Sequences

Geometric Sequences