Trigonometric graphs
Cambridge IGCSE Mathematics (0580) · Unit 6: Trigonometry · 9 flashcards
Trigonometric graphs is topic 6.4 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 6 — Trigonometry , alongside Trigonometric ratios, Sine and cosine rules and 3D trigonometry. In one line: Amplitude is the maximum displacement from the x-axis. For y = a*cos(x), the amplitude is |a|. Thus, the amplitude of y = 4cos(x) is 4.
This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator. It is a Supplement (Extended-tier) topic, so it appears only on the Extended-tier papers.
The deck below contains 9 flashcards — 4 definitions, 3 key concepts and 1 application card — covering the precise wording mark schemes reward. Use the 4 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.
The amplitude of the graph y = 4cos(x)
Amplitude is the maximum displacement from the x-axis. For y = a*cos(x), the amplitude is |a|. Thus, the amplitude of y = 4cos(x) is 4.
Questions this Trigonometric graphs deck will help you answer
- › Sketch the graph of y = sin(x) for 0° ≤ x ≤ 360°. Label key points.
- › Sketch the graph of y = cos(x) for 0° ≤ x ≤ 360°. Label key points.
- › Sketch the graph of y = tan(x) for -90° < x < 90°. Show any asymptotes.
- › The graph of y = cos(x) is stretched vertically by a factor of 2. Write the equation of the new graph.
Sketch the graph of y = sin(x) for 0° ≤ x ≤ 360°. Label key points.
The sine graph starts at (0,0), reaches a maximum of 1 at 90°, returns to 0 at 180°, reaches a minimum of -1 at 270°, and returns to 0 at 360°. Remember its 'wave' shape.
Sketch the graph of y = cos(x) for 0° ≤ x ≤ 360°. Label key points.
The cosine graph starts at (0,1), reaches 0 at 90°, reaches a minimum of -1 at 180°, returns to 0 at 270°, and ends at 1 at 360°. Think of it as a sine graph shifted left by 90 degrees.
What is the period of the graph y = sin(3x)?
The period is the length of one complete cycle. For y = sin(bx), the period is 360°/b. Therefore, the period of y = sin(3x) is 360°/3 = 120°.
What is the amplitude of the graph y = 4cos(x)?
Amplitude is the maximum displacement from the x-axis. For y = a*cos(x), the amplitude is |a|. Thus, the amplitude of y = 4cos(x) is 4.
Describe the transformation of y = sin(x) to y = sin(x) + 2.
The graph of y = sin(x) + 2 is a vertical translation of the graph y = sin(x) by 2 units upwards. All points on the graph are shifted up by 2.
Describe the transformation of y = cos(x) to y = cos(x - 30°).
The graph of y = cos(x - 30°) is a horizontal translation of the graph y = cos(x) by 30° to the right. The entire graph is shifted right by 30 degrees.
Sketch the graph of y = tan(x) for -90° < x < 90°. Show any asymptotes.
The tangent graph starts near -∞ at -90°, passes through (0,0), and approaches +∞ as x approaches 90°. It has vertical asymptotes at x = -90° and x = 90°.
What is the period of the graph y = tan(x)?
The period of the tangent function, y = tan(x), is 180°. The graph repeats every 180 degrees.
The graph of y = cos(x) is stretched vertically by a factor of 2. Write the equation of the new graph.
A vertical stretch by a factor of 2 means multiplying the entire function by 2. The equation of the new graph is y = 2cos(x).
Key Questions: Trigonometric graphs
What is the amplitude of the graph y = 4cos(x)?
Amplitude is the maximum displacement from the x-axis. For y = a*cos(x), the amplitude is |a|. Thus, the amplitude of y = 4cos(x) is 4.
Describe the transformation of y = sin(x) to y = sin(x) + 2.
The graph of y = sin(x) + 2 is a vertical translation of the graph y = sin(x) by 2 units upwards. All points on the graph are shifted up by 2.
Describe the transformation of y = cos(x) to y = cos(x - 30°).
The graph of y = cos(x - 30°) is a horizontal translation of the graph y = cos(x) by 30° to the right. The entire graph is shifted right by 30 degrees.
What is the period of the graph y = tan(x)?
The period of the tangent function, y = tan(x), is 180°. The graph repeats every 180 degrees.
More topics in Unit 6 — Trigonometry
Trigonometric graphs sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.
Cambridge syllabus keywords to use in your answers
These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.
Key terms covered in this Trigonometric graphs deck
Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.
Related Mathematics guides
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