Trigonometry – Graphs

Trigonometrical Graphs

Exact Solutions

Trigonometric Graphs and Equations

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)