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High School Trigonometry Math Course Outline

1.0 Credit

This honors level course will focus on the study of angles; the trigonometry of angles and real numbers; the trigonometric functions and their inverses including their graphs; solutions of right and oblique triangles; verification of fundamental identities and analytic trigonometry; addition, subtraction and multiple angle formulas; the laws of sines and cosines; vectors and the dot and cross product; complex numbers, De Moivre’s Theorem and nth roots of complex numbers; polar coordinates and equations. The course will also include the study of functions including exponential and logarithmic functions.

TRIGONOMETRIC FUNCTIONS

• Extend the domain of trigonometric functions using the unit circle.
• Model periodic phenomena with trigonometric functions.
• Prove and apply trigonometric identies.

THE COMPLEX NUMBER SYSTEM

• Perform arithmetic operations with complex numbers.
• Represent complex numbers and their operations on the complex plane.
• Use complex numbers in polynomial identies and equations.

VECTOR & MATRIX QUANTITIES

• Represent and model with vector quantities.
• Perform operations on vectors.

SIMILARITY, RIGHT TRIANGLES TRIGONOMETRY

• Define trigonometric ratios and solve problems involving right triangles.
• Apply trigonometry to general triangles.

1- Introduction

• Introduction
• Course Description
• Pretest
• Assignment: Pretest
• MLA Formatting Word 2007
• MLA Documentation Updates
• MLA Citation
• MLA Incorporating Sources
• Completing Math Assessments

2- Angles & Triangles

• Angles & Angle Measures
• Handout: Angles & Angle Measures Worksheet
• Assignment: Angles & Angle Measures
• Worksheet: Converting Angle Measures
• Triangle Review
• Handout: Triangle Review Worksheet
• Assignment: Triangle Review
• Pythagorean Theorem
• Handout: Pythagorean Theorem Worksheet
• Assignment: Pythagorean Theorem
• Special Right Triangles
• Handout: Special Right Triangles Worksheet
• Assignment: Special Right Triangles
• Basic Trignometric Ratios
• Handout: Basic Trigonometric Ratios Worksheet
• Assignment: Basic Trigonometric Ratios
• Inverse Trigonometric Ratios
• Worksheet: Inverse Trigonometric Ratios
• Laws of Sine & Cosine
• Handout: Law of Sines & Cosines Worksheet
• Assignment: Law of Sines & Cosines
• The Unit Circle
• Handout: Unit Circle
• Handout: Finding Trig Values
• Handout: Evaluating Trig Functions Worksheet
• Assignment: Evaluating Trig Functions

3- Graphs of Trigonometric Functions

• Graphs of Sine & Cosine
• Handout: Graphs of Sine & Cosine Worksheet
• Assignment: Graphs of Sine & Cosine
• Linear & Angular Velocity
• Handout: Linear & Angular Velocity Worksheet
• Assignment: Linear & Angular Velocity
• Graphs of Other Trig Functions
• Handout: Cotangent Graph Exploration
• Assignment: Cotangent Graph Exploration
• Translations of Trig Functions
• Handout: Translations of Trig Functions Worksheet
• Assignment: Translations of Trig Functions
• Applications of Trig Functions
• Handout: Sinusoidal Applications Worksheet
• Essay: Real-World Applications
• Assignment: Sinusoidal Applications

4- Trigonometric Identities

• Fundamental Trigonometric Identities
• Handout: Fundamental Trigonometric Identities Worksheet
• Assignment: Fundamental Trigonometric Identities
• Proving Trigonometric Identities
• Handout: Proving Trig Identities Worksheet
• Assignment: Proving Trig Identities
• Sum & Difference Identities
• Handout: Sum & Difference Identities Worksheet
• Assignment: Sum & Difference Identities
• Essay: Sum & Difference Identities Short Answer
• Double-Angle & Half-Angle Identities
• Handout: Double & Half-Angle Identities Worksheet
• Assignment: Double & Half-Angle Identities
• Essay: Double & Half-Angle Identities Short Answer
• Solving Trigonometric Equations
• Handout: Solving Trig Equations Worksheet
• Assignment: Solving Trig Equations

5- Mid-Term Exam

• Midtest
• Assignment: Midtest
• Handout: Trigonometry Mid-Term Exam
• Assignment: Trigonometry Mid-Term Exam

6- Inverse Trig Functions

• Review: Basic Inverse Trig Functions
• Handout: Inverse Review Worksheet
• Assignment: Inverse Review
• Graphs of Inverse Trig Functions
• Handout: Inverse Trig Graphs Worksheet
• Assignment: Inverse Trig Graphs
• Inverse Trig Properties
• Handout: Inverse Trig Properties Worksheet
• Assignment: Inverse Trig Properties
• Area of Triangles
• Handout: Area of Triangles Worksheet
• Assignment: Area of Triangles

7- Vectors

• Introduction to Vectors
• Handout: Introduction to Vectors Worksheet
• Assignment: Introduction to Vectors
• Geometric Vectors: Adding & Subtracting
• Handout: Geometric Vectors
• Assignment: Geometric Vectors
• Algebraic Vectors
• Handout: Algebraic Vectors Worksheet
• Assignment: Algebraic Vectors

8- The Polar System

• Polar Coordinates
• Handout: Polar Coordinates Worksheet
• Assignment: Polar Coordinates
• Graphing Polar Equations
• Handout: Graphing Polar Equations Worksheet
• Assignment: Graphing Polar Equations
• Polar & Rectangular Coordinates
• Handout: Converting Polar & Rectangular Equations Worksheet
• Worksheet: Converting Polar & Rectangular Coordinates
• Assignment: Converting Polar & Rectangular Equations
• Complex Numbers
• Handout: Operations With Complex Numbers Worksheet
• Assignment: Operations With Complex Numbers
• Polar Form of Complex Numbers
• Handout: Polar Form of Complex Numbers Worksheet
• Assignment: Polar Form of Complex Numbers
• Complex Numbers in Polar Form: Products & Quotients
• Handout: Products & Quotients Worksheet
• Assignment: Products & Quotients
• De Moivre’s Theorem
• Handout: De Moivre’s Theorem Worksheet
• Assignment: De Moivre’s Theorem

9- Final Exam

• Post-test
• Assignment: Post-test
• Handout: Trigonometry Final Exam
• Assignment: Final Exam

10- Course Survey

• Handout: Course Survey
• Assignment: Course Survey
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