# Trigonometry – Graphs

Students learn how to visualise and sketch the Sine, Cosine and Tangent graphs.  They use these graphs to find all the solutions to trigonometric equations.  Learning progresses from this to finding the exact solutions to Sine, Cos and Tan of 30, 45, 60 and 90 using an equilateral and right-angled triangle.

This unit takes place in Term 2 of Year 11 and follows on from trigonometry in non-right-angled triangles.

##### Revision Lessons

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°; know the exact value of for = 0°, 30°, 45°, 60°
• 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 at that can be used to find additional solutions equations.
• Trigonometric ratios of 30°, 45° and 60° have exact forms that can be calculated using the special triangles.
• The relationship Tanθ = Sinθ/Cosθ can be seen fro 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)

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