Students begin by exploring angle measurement in degrees and radians before developing the trigonometric ratios used to solve right triangles. They investigate the six trigonometric functions, apply inverse trigonometric functions to determine unknown angles, and solve practical problems involving angles of elevation, depression, navigation, and measurement. This unit establishes the essential concepts that underpin the remainder of the course.
This unit extends trigonometry beyond right triangles by introducing the unit circle and defining trigonometric functions for all angles. Students investigate exact values, domains and ranges, graph the sine, cosine, and tangent functions, and analyse transformations including changes in amplitude, period, and phase shift. Inverse trigonometric functions are introduced to strengthen students' understanding of function behaviour.
Students develop the algebraic techniques needed to manipulate trigonometric expressions and solve increasingly sophisticated problems. They investigate fundamental identities, angle sum and difference identities, double-angle and half-angle identities, and apply these relationships to verify identities and solve trigonometric equations. Logical reasoning and mathematical proof play a central role throughout the unit.
Students expand their problem-solving skills to include any triangle by applying the Law of Sines and the Law of Cosines. They investigate ambiguous cases, calculate areas of oblique triangles, solve navigation and surveying problems, and apply trigonometry to practical measurement situations. Emphasis is placed on selecting appropriate solution methods and interpreting results within real-world contexts.
The final unit demonstrates how trigonometry extends far beyond geometry into advanced mathematics and science. Students develop trigonometric models for periodic phenomena, investigate polar coordinates and parametric curves, explore connections with complex numbers, and apply trigonometry to physics, engineering, architecture, and technology. The course concludes with comprehensive problem solving that integrates concepts from every unit.
Subtopics
Trigonometric Modelling
Polar Coordinates and Parametric Curves
Complex Numbers and Trigonometry
Trigonometry in Science and Engineering
Comprehensive Problem Solving
By the end of this course, students will be able to analyse and solve problems involving trigonometric functions, identities, equations, and triangles using both algebraic and geometric methods. They will confidently interpret graphs, model periodic behaviour, apply trigonometry to real-world situations, and communicate mathematical reasoning with precision. These skills provide a strong foundation for further study in vectors, precalculus, calculus, physics, engineering, computer science, and many other STEM disciplines.