Course objectives:

This online course is designed to provide educators with a comprehensive understanding of trigonometry through a functional lens. The course aims to seamlessly bridge the fundamental concepts of functions into the realm of trigonometry.

The course begins with a review and extension of fundamental functions introduced in Grade 10, emphasizing their relevance to trigonometry. Teachers will explore the components, domain, codomain and range, of a function, thereby laying a solid foundation for the application of functions in trigonometric contexts.

As the course progresses, participants will delve into the functional properties of trigonometric ratios, identities, and equations. Special attention will be given to the periodic feature of trigonometric functions, emphasizing real-world applications and problem-solving strategies. Practical examples and classroom activities will be integrated to enhance pedagogical skills, ensuring that teachers are well-equipped to engage students in the exploration of trigonometric concepts.

 Skills focus:

• Use unit circle to demonstrate calculation (determination) of trigonometric ratios, especially for angles ϴ ≥ 90°.

• Explore methods (strategies) for deriving and proving (justifying) trigonometric identities

• Techniques for solving trigonometric equations by using the periodic feature of the trigonometric functions

Key Course Components:

Review of fundamentals of Functions:

• Explore the function concept, and provide a mathematical description (definition)..

• Provide very simple, abstract as well as typical and familiar CAPS examples of functions.

• Explore more general notions –– basic non-functions and relations, (e.g. inequalities ≤).

Introduction to Trigonometry:

• Unit circle (and comparing degree and radian measure –– in brief).

• Trigonometric ratios: defining sine, cosine, tangent, cotangent, secant, and cosecant via unit circle.

• Linking the trigonometric ratio via a unit circle to trigonometric functions and graphs.

Functional Properties of Trigonometry:

• Derive and use trigonometric identities

• Derive and use reduction formulae, towards simplification of expressions 

• Solve and derive general solutions of trigonometric equations

• Explore graphs of trigonometric functions, especially features such as periodicity, amplitude and use in solution of trigonometric equations. .

• Applications of trigonometry in real-world examples.

Pedagogical Strategies and Classroom Applications:

• Effective teaching methodologies for trigonometry.

• Incorporating technology in trigonometry lessons (e.g. use of GeoGebra).

• Practical activities and demonstrations to enhance student understanding.

By the end of this course teachers will have gained a deep understanding of the functional aspects of trigonometry and will be well-prepared to guide their learners through the complexities of this mathematical domain. The integration of practical teaching strategies ensures that educators leave the course with the tools necessary to create an engaging and enriching learning experience for their learners.