This IB Maths AA SL Topic 3.5 – Trigonometry and the Unit Circle resource develops students’ understanding of sine, cosine, and tangent through the geometry of the unit circle. It begins by defining sin(θ) and cos(θ) as coordinates on a circle of radius 1 and showing how tan(θ) can be expressed as sin(θ)/cos(θ). Students also review degree–radian conversion and use special right triangles to derive exact trigonometric values for key angles, including 0, π/6, π/4, π/3, and π/2.

The lesson then extends these ideas around the full unit circle, helping students identify the signs of trigonometric functions in each quadrant and use relationships between related angles to determine exact values. Students also explore the connection between tangent and the gradient of a line through the origin, including equations of the form y = tan(θ)x. The resource concludes by extending the sine rule to the ambiguous case, showing how two different triangles may satisfy the same given information. With clear diagrams, exact-value tables, worked examples, quadrant practice, line-equation problems, and fully worked solutions, this resource helps SL students build strong conceptual and procedural understanding of trigonometry in line with IB Mathematics AA expectations.