Trigonometric Ratios

Trigonometric Ratios Lessons

4 Part Lesson
Transforming Trigonometric Graphs
4 Part Lesson
Proving Trigonometric Identities
4 Part Lesson
Problems with Non-Right-Angled Triangles
4 Part Lesson
Area of Non-Right-Angled Triangles
4 Part Lesson
Problems Involving the Cosine Rule
4 Part Lesson
Problems involving the Sine Rule

Prerequisite Knowledge

  • Right-angled trigonometry including Sin θ = O/H, Cos θ = A/H and Tan θ = O/A.
  • Know and apply Pythagoras’ Theorem
  • Visualise the graphs of y = Sin θ and y = Cos θ between the range -360 ≤ θ ≤ 360.
  • Transform basic 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 be able to use the sine, cosine and tangent functions; their graphs, symmetries and periodicity.

Teaching Points

  • 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.


  • 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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