This IB Maths AA SL Topic 3.6 – The Pythagorean Identity resource develops students’ understanding of fundamental trigonometric identities and the relationships between sine, cosine, and tangent. It begins by deriving the Pythagorean identity sin²(θ) + cos²(θ) = 1 from the geometry of the unit circle, helping students connect the algebraic identity to the Pythagorean theorem.

The lesson then introduces the double-angle identities sin(2θ) = 2sin(θ)cos(θ) and cos(2θ) = cos²(θ) - sin²(θ), with optional proofs included for advanced students. Students practise using quadrants, right triangles, and exact values to calculate one trigonometric ratio from another without first finding the angle. They also apply the identities to find values such as sin(2x) and cos(2θ), simplify trigonometric expressions, and interpret the signs of ratios in different quadrants. With clear geometric explanations, worked proofs, diagram-based reasoning, practice questions, and fully worked solutions, this resource helps SL students build strong trigonometric fluency in line with IB Mathematics AA expectations.