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.

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