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This topic covers the graphs of sin, cos and tan, their periods, amplitudes and symmetries, and how transformations such as y = a sin(bx + c) + d stretch, shift and reflect them. It appears across A-Level and iAL Pure Maths with the major exam boards. Learn it free on eClassroom through guided worked examples and instantly-marked exam-style questions.
How you do it
Start from the shape of sine, cosine or tangent, then apply the transformations in order. The number in front changes amplitude; the number multiplying the angle changes the period, dividing 360 by it. Shifts inside the bracket move horizontally the opposite way to their sign.
Before you start
Get graph transformations and trig ratios straight before you begin. From here the path runs to solving trigonometric equations.
What you learn
The graphs of sin, cos and tan behave differently — cosine peaks at 0°, tangent has asymptotes and repeats every 180° with no amplitude at all. and problem solving with trig graphs. y=sinθ and y=cosθ both have amplitude 1 and period 360°, but cosine peaks at θ=0° while sine starts at the origin. For tangent there is no amplitude to stretch — instead a horizontal stretch moves the asymptotes, and a translation shifts them sideways. A tangent curve has no amplitude to read — use its asymptote spacing instead. The course works through the three graphs and their features, transformations of the trig graphs, finding the function from its graph, how many solutions? Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Trig Graphs & Transformations is a Trigonometry topic in the A-level syllabus, covered here at the AS year. It runs to 5 concepts, each followed by a check, with 5 worked examples along the way. Nearby topics in the same strand are Trig Identities (C12), Trig Ratios & Exact Values, Addition Formulae, Double Angle Formulae and Further Trig Equations. For unlimited practice, the Trigonometry revision engine builds new questions on demand and records your accuracy.
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