Grade 12 Trigonometry Online High School Course
Course Overview
This Grade 12 Trigonometry online course is an honors-level mathematics course that focuses on the study of angles, trigonometric functions, and their real-world applications. Students examine relationships between angles and real numbers while developing a deeper understanding of trigonometric concepts used in advanced mathematics. The course explores trigonometric functions and their inverses, including graphical representations and problem-solving applications. Students analyze both right and oblique triangles and apply trigonometry to a variety of mathematical contexts, De Moivre’s Theorem and nth roots of complex numbers; polar coordinates and equations.
What Students Learn
Throughout the course, students develop a strong foundation in trigonometric reasoning and mathematical analysis. Emphasis is placed on understanding trigonometric relationships, solving equations, interpreting graphs, and applying concepts to both theoretical and practical problems
Learning Approach
Instruction is delivered through structured lessons, guided practice, and problem-solving activities that encourage independent learning and critical thinking. Students apply trigonometric concepts across multiple representations, including algebraic, graphical, and geometric models.
Trigonometry Course Outline (1.0 Credit)
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.
Course Outline
Introduction
- Introduction
- Course Description
- Pretest
- Assignment: Pretest
- MLA Formatting Word 2007
- MLA Documentation Updates
- MLA Citation
- MLA Incorporating Sources
- Completing Math Assessments
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
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
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
Mid-Term Exam
- Midtest
- Assignment: Midtest
- Handout: Trigonometry Mid-Term Exam
- Assignment: Trigonometry Mid-Term Exam
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
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
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
Final Exam
- Post-test
- Assignment: Post-test
- Handout: Trigonometry Final Exam
- Assignment: Final Exam
Course Survey
- Handout: Course Survey
- Assignment: Course Survey
