| 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).
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.
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
How are the sine and cosine graphs related?
The cosine graph is the sine graph shifted 90° to the LEFT.
cos x = sin(x + 90°) OR sin x = cos(x - 90°)
Both have the same shape, amplitude and period — the cosine graph simply starts at its maximum (1) rather than at zero.
Describe the key features of the sine graph y = sin x
Shape: smooth wave (S-shaped repeating curve)
Amplitude: 1 (max value = 1, min value = -1)
Period: 360° (repeats every 360°)
Passes through: (0, 0), (90°, 1), (180°, 0), (270°, -1), (360°, 0)
Symmetry: origin symmetry (odd function)