Trigonometry
Table of Contents
(working draft -- revised 05/25/06)
Chapter 1: An Introduction to Trigonometry
Preview
1.1Angle Measure, Special Triangles and Special Angles
1.2The Trigonometry of Right Triangles
• Mid-Chapter Check
• Reinforcing Basic Concepts: The Area of a Triangle
1.3Trigonometry and the Coordinate Plane
1.4Unit Circles and Trigonometric Functions
Summary and Concept Review
Mixed Review
Practice Test
Calculator Exploration and Discovery:Signs, Quadrants, and Reference Angles
Strengthening Core Skills: More on Radians
Chapter 2: Trigonometric Graphs and Models
2.1Graphs of Sine and Cosine Functions
2.2Graphs of Tangent and Cotangent Functions
• Mid-Chapter Check
• Reinforcing Basic Concepts: Trigonometric Potpourri
2.3Transformations and Applications of Trigonometric Graphs
2.4Trigonometric Models
Summary and Concept Review
Mixed Review
Practice Test
Calculator Exploration and Discovery:Variable Amplitudes and Modeling the Tides
Strengthening Core Skills: Standard Angles, Reference Angles, and the Trig Functions
Cumulative Review 1 - 2
Chapter 3: Trig Identities: Their Purpose, Place, and Application
Preview
3.1Fundamental Identities and Families of Identities
3.2Constructing and Verifying Identities
• Mid-Chapter Check
• Reinforcing Basic Concepts: Understanding Identities
3.3The Sum and Difference Identities
3.4Double Angle, Half Angle, and Product-to-Sum identities
Summary and Concept Review
Mixed Review
Practice Test
Calculator Exploration and Discovery: Seeing the Beats as the Beats Go On
Strengthening Core Skills: Connections and Relationships
Cumulative Review 1 - 3
Chapter 4: Trigonometric Equations
Preview
4.1One-to-One and Inverse Functions
4.2The Inverse Trig Functions and their Application
4.3Solving Basic Trig Equations
• Mid -Chapter Check
• Reinforcing Basic Concepts: More on Equation Solving
4.4General Trig Equations and Applications
4.5Parametric Equations and Graphs
Summary and Concept Review
Mixed Review
Practice Test
Calculator Exploration and Discovery: More on Parametric Equations
Strengthening Core Skills: Trigonometric Equations and Inequalities
Cumulative Review 1 - 4
Chapter 5: Applications of Trigonometry
Preview
5.1Oblique Triangles and the Law of Sines
5.2Law of Sines and the Ambiguous Case
5.3The Law of Cosines
5.4Vectors and Vector Diagrams
• Mid -Chapter Check
• Reinforcing Basic Concepts: Scale Drawings and the Laws of Sine and Cosine
5.5Vectors Applications and the Dot Product
5.6Complex Numbers
5.7Complex Numbers in Trigonometric Form
5.8Demoivre’s Theorem and the Nth Roots Theorem
Summary and Concept Review
Mixed Review
Practice Test
Calculator Exploration and Discovery: Investigating Projectile Motion
Strengthening Core Skills: Vectors and Static Equilibrium
Cumulative Review 1 - 5
Chapter 6: Conic Sections and Polar Coordinates
Preview
6.1The Circle and the Ellipse
6.2The Hyperbola
6.3Foci and the Analytic Ellipse and Hyperbola
• Mid-Chapter Check
• Reinforcing Basic Concepts: Ellipses and Hyperbolas with a, b rational
6.4The Analytic Parabola
6.5Polar Coordinates, Equations, and Graphs
6.6More on the Conic Sections: Rotation of Axes and Polar Form
Summary and Concept Review
Mixed Review
Practice Test
Calculator Exploration and Discovery: Conic Rotations in Polar Form
Strengthening Core Skills: Simplifying and Streamlining Computations
for the Rotation of Axes
Cumulative Review 1 – 6
Appendix I: Transformations of a Basic Graph
Appendix II: Solving Equations Graphically
Appendix III: Regression and Calculator Use
Appendix IV: Miscellaneous Algebra Review
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