GraphsDeep Dive

Key Points to Know by Heart

Part of Trig GraphsGCSE Mathematics

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. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. 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.

Topic position

Section 4 of 11

Practice

11 questions

Recall

11 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 ±∞

Keep building this topic

Read this section alongside the surrounding pages in Trig Graphs. That gives you the full topic sequence instead of a single isolated revision point.

Practice Questions for Trig Graphs

What is the period of the graph y = sin x?

  • A. 90°
  • B. 180°
  • C. 360°
  • D. 720°
1 markfoundation

Explain the relationship between the graphs of y = sin x and y = cos x.

2 markshigher

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.

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