Trigonometric Ratios

Scheme of work: Year 12 A-Level: Pure 1: Trigonometric Ratios

Prerequisite Knowledge

  • Right-angled trigonometry, including Sin x¸ = O/H, Cos x¸ = A/H and Tan x¸ = O/A.
  • Know and apply Pythagoras Theorem
  • Visualise the graphs of y = Sin x¸ and y = Cosx¸ between the range -360 <= x <= 360.
  • Transform essential graphical functions.
  • Know exact trigonometric solutions from an equilateral triangle and isosceles right-angled triangle.
  • Construct and interpret scale drawings involving bearings.

Success Criteria

  • Understand and be able to use the definitions of sine, cosine and tangent for all arguments;
  • understand and be able to use the sine and cosine rules;
  • understand and be able to use the area of a triangle in the form Area = ½ ab SinC
  • understand and use the sine, cosine and tangent functions; their graphs, symmetries and periodicity.

Key Concepts

  • Students should prove the Sine, Cosine and Area rules using right-angled trigonometry.
  • Problems should involve multiple rules for the challenge.
  • The sine rule applies when a matching pair of angle and length is given.
  • The cosine rule can be used when either all three lengths of a triangle is given. Or when two lengths either side of an angle are given.
  • The area rule needs an angle between two available lengths.
  • Application of the sine and cosine rules is often linked to scale drawings and triangles with algebraic lengths.

Common Misconceptions

  • Students often mislabel their diagrams, so the angle and opposite edge do not have the respective upper- and lower-case letters. 
  • Problems involving an angle found using the Sine Rule can have two solutions.
  • When transforming graphs, students should use sketched diagrams are mistakes are often made when working algebraically.

Trigonometric Ratios Resources

Mr Mathematics Blog

Planes of Symmetry in 3D Shapes

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

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GCSE Trigonometry Skills & SOH CAH TOA Techniques

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