Trigonometry

Following a review of foundational algebra topics (primarily functions and the related topics of graphs, transformations, combinations, and inverses) the great power of Trigonometry in a “mathematical toolbox” is unveiled as the course continues into degree and radian measure, trig ratios, graphs of trig functions, trigonometric identities and equations, and vectors. Exponential and logarithmic functions are included, along with the study of conics, parametric equations, and polar coordinates. Use of the graphing calculator is emphasized.

Table of Contents

Chapter P – PREREQUISITES

P.1 Review of Real Numbers and Their Properties
P.2 Solving Equations
P.3 The Cartesian Plane and Graphs of Equations
P.4 Linear Equations in Two Variables
P.5 Functions
P.6 Analyzing Graphs of Functions
P.7 A Library of Parent Functions
P.8 Transformations of Functions
P.9 Combinations of Functions: Composite Functions
P.10 Inverse Functions

Chapter 1 – TRIGONOMETRY

1.1 Radian and Degree Measure
1.2 Trigonometric Functions: The Unit Circle
1.3 Right Triangle Trigonometry
1.4 Trigonometric Functions of Any Angle
1.5 Graphs of Sine and Cosine Functions
1.6 Graphs of Other Trigonometric Functions
1.7 Inverse Trigonometric Functions
1.8 Applications and Models

Chapter 2 – ANALYTIC TRIGONOMETRY

2.1 Using Fundamental Identities
2.2 Verifying Trigonometric Identities
2.3 Solving Trigonometric Equations
2.4 Sum and Difference Formulas
2.5 Multiple-Angle and Product-to-Sum Formulas

Chapter 3 – ADDITIONAL TOPICS IN TRIGONOMETRY

3.1 Law of Sines
3.2 Law of Cosines
3.3 Vectors in the Plane
3.4 Vectors and Dot Products

Chapter 4 – COMPLEX NUMBERS

4.1 Complex Numbers
4.2 Complex Solutions of Equations
4.3 Trigonometric Form of a Complex Number
4.4 DeMoivre’s Theorem

Chapter 5 – EXPONENTIAL AND LOGARITHMIC FUNCTIONS

5.1 Exponential Functions and Their Graphs
5.2 Logarithmic Functions and Their Graphs
5.3 Properties of Logarithms
5.4 Exponential and Logarithmic Equations
5.5 Exponential and Logarithmic Models

Chapter 6 – TOPICS IN ANALYTIC GEOMETRY

6.1 Lines
6.2 Introduction to Conics: Parabolas
6.3 Ellipses
6.4 Hyperbolas
6.5 Rotation of Conics
6.6 Parametric Equations
6.7 Polar Coordinates
6.8 Graphs of Polar Equations
6.9 Polar Equations of Conics

Sample Videos from this Course