Course Title: Fundamentals of Trigonometry
Course Description: This course provides a comprehensive introduction to trigonometry, covering fundamental concepts such as trigonometric functions, identities, equations, and their applications in geometry and physics. Students will develop a strong understanding of trigonometric principles and problem-solving skills.
Course Outline:
- Week 1: Introduction to Trigonometry
- Definition and history of trigonometry
- Trigonometric ratios (sine, cosine, tangent)
- Degrees and radians, converting between them
- Week 2: Trigonometric Functions
- Graphs of trigonometric functions
- Periodicity and amplitude
- Phase shifts and vertical shifts
- Week 3: Trigonometric Identities I
- Pythagorean identities
- Sum and difference identities
- Double-angle and half-angle identities
- Week 4: Trigonometric Identities II
- Product-to-sum and sum-to-product identities
- Cofunction identities
- Verifying and proving trigonometric identities
- Week 5: Trigonometric Equations
- Solving basic trigonometric equations
- Solving trigonometric equations with identities
- Applications of trigonometric equations
- Week 6: Right Triangle Trigonometry
- Solving right triangles using trigonometric ratios
- Applications in geometry and physics (heights and distances)
- Angle of elevation and angle of depression problems
- Week 7: Law of Sines and Law of Cosines
- Derivation and applications of the Law of Sines
- Derivation and applications of the Law of Cosines
- Solving oblique triangles
- Week 8: Trigonometric Functions in the Unit Circle
- Definitions of sine and cosine in the unit circle
- Finding exact values of trigonometric functions
- Circular functions and their properties
- Week 9: Polar Coordinates and Complex Numbers
- Introduction to polar coordinates
- Converting between polar and rectangular coordinates
- Applications of polar coordinates in trigonometry
- Week 10: Applications of Trigonometry
- Trigonometry in physics (waves, oscillations)
- Trigonometry in engineering (vectors, forces)
- Trigonometry in astronomy (stellar parallax, celestial navigation)
Course Assignments:
- Weekly problem sets and quizzes
- Trigonometric function graphing and analysis
- Trigonometric identities and equations exercises
- Right triangle trigonometry problems
- Applications of trigonometry in real-world scenarios
- Final project: Trigonometry application project (e.g., modeling a real-life problem using trigonometric concepts)
Course Materials:
- Textbook: “Trigonometry” by Michael Sullivan
- Trigonometry software and graphing tools
- Online tutorials and interactive resources
- Practice worksheets and exercises
- Real-world examples and applications of trigonometry
Assessment:
- Quizzes and exams covering trigonometry concepts and techniques
- Problem-solving assignments and projects
- Trigonometric function and identity proficiency assessment
- Final project evaluation based on trigonometry applications and analysis
- Class participation and engagement in discussions and activities
Prerequisites: A solid foundation in algebra and geometry is required. Familiarity with basic trigonometric concepts (sine, cosine, tangent) is recommended.