Three Graphs at a Glance
- sin x: starts (0, 0), period 360°, amp 1
- cos x: starts (0, 1), period 360°, amp 1
- tan x: period 180°, asymptotes at 90°, 270°
- cos x = sin(x + 90°) — shifted left 90°
Transformations
- a sin x → amplitude = a
- sin(nx) → period = 360°/n
- sin x + c → vertical shift up c
- sin(x − a°) → shift right a°
Key Vocabulary
- Amplitude: distance from midline to max/min
- Period: x-length of one full cycle
- Phase shift: horizontal translation
- Asymptote: vertical line where tan is undefined
Common Errors
- Period of sin(2x) = 720° (should be 180°)
- Only finding one solution to sin x = k
- Thinking cos x starts at 0 (it starts at 1)
- Phase shift direction — inside bracket means opposite
Key Formulas
- sin x: period 360°, amplitude 1, starts at (0, 0)
- cos x: period 360°, amplitude 1, starts at (0, 1)
- tan x: period 180°, asymptotes at 90°, 270°, …
- sin(2x): period = 360° ÷ 2 = 180°; a sin x: amplitude = a
This topic summary covers Knowledge Organiser: 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 11 of 11 in this topic. Use this topic summary 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)