Trigonometry – Graphs

Scheme of work: GCSE Higher: Year 11: Term 1: Trigonometry – Graphs

Prerequisite Knowledge

  • Know the trigonometric ratios.
  • Apply them to find angles and lengths in right-angled triangles and, where possible, general triangles in two and three dimensional figures

Success Criteria

  • Know the exact values of and for = 0°, 30°, 45°, 60° and 90°;
  • Recognise, sketch and interpret graphs of trigonometric functions (with arguments in degrees) y = sin x , y = cos x and y = tan x for angles of any size

Key Concepts

  • Trigonometric graphs have lines of symmetry that can be used to find additional solutions to equations.
  • Trigonometric ratios of 30°, 45° and 60° have exact forms that can be calculated using the special triangles.
  • The relationship Tan x¸ = Sin x, Cos x¸ can be seen from the asymptotes in the tan graph

Common Misconceptions

  • Students often forget to rationalise Sin45° and Cos45°.
  • When solving trigonometric equations students often forget to use the graphs to include all solutions.
  • In examinations students often confuse the coordinates, e.g., (0,180) with (180,0)

Trigonometric Graphs Resources

Mr Mathematics Blog

Planes of Symmetry in 3D Shapes

Planes of Symmetry in 3D Shapes for Key Stage 3/GCSE students.

Use isometric paper for hands-on learning and enhanced understanding.

GCSE Trigonometry Skills & SOH CAH TOA Techniques

Master GCSE Math: Get key SOH-CAH-TOA tips, solve triangles accurately, and tackle area tasks. Ideal for students targeting grades 4-5.

Regions in the Complex Plane

Explore Regions in the Complex Plane with A-Level Further Maths: inequalities, Argand diagrams, and geometric interpretations.