This deep dive covers Transformations of Trig Graphs within Trig Graphs for GCSE Mathematics. Revise Trig Graphs in Graphs for GCSE Mathematics with 11 exam-style questions and 11 flashcards. Use this page as part of a wider topic revision path rather than treating it as an isolated fact. It is section 5 of 11 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 5 of 11
Practice
11 questions
Recall
11 flashcards
Transformations of Trig Graphs
| Transformation | Effect | Example |
|---|---|---|
| y = a sin x | Amplitude = |a| (vertical stretch) | y = 3 sin x → oscillates −3 to 3 |
| y = sin(nx) | Period = 360°/n (horizontal compression) | y = sin(2x) → period = 180° |
| y = sin x + c | Vertical translation up c units | y = sin x + 2 → midline at y = 2 |
| y = sin(x − a°) | Horizontal translation right a° (phase shift) | y = sin(x − 30°) → shifts right 30° |
| y = −sin x | Reflection in x-axis (flips upside down) | y = −sin x → inverted wave |
Remember: changes inside the brackets → opposite direction (sin(x + a) goes LEFT); changes outside → in the expected direction (sin x + a goes UP).
Keep building this topic
Read this section alongside the surrounding pages in Trig Graphs. That gives you the full topic sequence instead of a single isolated revision point.
Practice Questions for Trig Graphs
What is the period of the graph y = sin x?
Explain the relationship between the graphs of y = sin x and y = cos x.
Quick Recall Flashcards
11 questions on Trig Graphs — practise free
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