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.
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).
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)