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 = Â½ 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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