This deep dive covers Key Points to Know by Heart 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 4 of 11 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Key Points to Know by Heart
Sine graph y = sin x
- Starts at (0°, 0) — passes through the origin
- Reaches maximum 1 at x = 90°
- Returns to 0 at x = 180°
- Reaches minimum −1 at x = 270°
- Returns to 0 at x = 360° (one full cycle complete)
Cosine graph y = cos x
- Starts at (0°, 1) — maximum at origin
- Crosses zero at x = 90°
- Reaches minimum −1 at x = 180°
- Returns to 0 at x = 270°
- Returns to 1 at x = 360° (one full cycle complete)
Relationship: cos x = sin(x + 90°) — the cosine graph is the sine graph shifted 90° to the left.
Tangent graph y = tan x
- Period of 180° (not 360°)
- Vertical asymptotes at x = 90°, 270°, −90°, 450°, ...
- Passes through (0°, 0), (45°, 1), (135°, −1)
- Has no maximum or minimum — goes to ±∞
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.