- Learn the 5 key points for each wave (0°, 90°, 180°, 270°, 360°) — you can sketch from these alone
- Period vs amplitude: period is the horizontal width of one cycle; amplitude is the vertical height from the midline
- Multiple solutions: if asked to solve sin x = k or cos x = k in a range, always check for a second solution using symmetry
- tan at 90°: always show the asymptote — the tan graph does NOT cross x = 90°
- Transformation direction: sin(x + 30°) moves LEFT by 30° (inside bracket = opposite direction)
This exam tips covers Exam Tips for Trigonometric 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 8 of 11 in this topic. Treat this as a marking guide for what examiners are looking for, not just a fact list.
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
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)
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.