Who this is for: Cambridge IGCSE Mathematics (0580/0607) students who want Trigonometric Graphs — sketching and reading sin, cos and tan curves — to become a reliable source of marks instead of shapes they draw from memory without key points.
What query it owns: how to understand and revise Trigonometric Graphs in Cambridge IGCSE Mathematics.
Why this is safe: this page owns the Trigonometric Graphs revision-guide angle, while Tutopiya’s Trigonometric Graphs subtopic page owns the learning resource and the free Trigonometric Graphs quiz owns the practice.

Trigonometric Graphs appear in the Trigonometry unit of Cambridge IGCSE Mathematics (0580/0607). Whenever a question asks you to sketch y = sin x, y = cos x or y = tan x, or to read solutions from a graph, examiners expect you to plot key points accurately and understand amplitude and period. This guide explains the curves that actually appear, how to sketch them by hand, and where to practise each skill.

Key takeaways

• y = sin x and y = cos x oscillate between −1 and 1 with period 360° (one full wave every 360°).
• y = tan x has vertical asymptotes at 90°, 270°, … and repeats every 180°.
• Plot key points at 0°, 90°, 180°, 270°, 360° before sketching the smooth curve.
• For y = a sin x or y = a cos x, the amplitude is |a|; the period stays 360°.

What are Trigonometric Graphs in Cambridge IGCSE Maths?

Trigonometric Graphs show how sin, cos and tan values change as the angle x increases from 0° to 360° and beyond. In Cambridge IGCSE Mathematics you must sketch these curves, read angles from graphs, and understand how multiplying by a constant changes the amplitude. They connect to trigonometric equations, where solutions are found from graph intersections.

You can read the full explanation, worked examples and notes on Tutopiya’s Trigonometric Graphs subtopic page before you attempt questions.

The core ideas you must master

These four ideas appear again and again. Learn what each one means and the exam phrasing that signals it.

Idea	What it means	How the exam uses it
sin x graph	Starts at 0; peaks at 90°; 0 at 180°; min at 270°	“Sketch y = sin x for 0° ≤ x ≤ 360°“
cos x graph	Starts at 1; 0 at 90°; −1 at 180°	“Sketch y = cos x”
tan x graph	Asymptotes at 90°, 270°; period 180°	“Sketch y = tan x”
Amplitude	Height of wave;	a

How to sketch trigonometric graphs — step by step

The safest method works for sin, cos and tan.

1. Draw axes — x from 0° to 360° (or the range stated); y from −1 to 1 (or wider if amplitude > 1).
2. Mark key angles on the x-axis: 0°, 90°, 180°, 270°, 360°.
3. Plot exact values — sin 0° = 0, sin 90° = 1, sin 180° = 0, sin 270° = −1.
4. Join with a smooth curve — not straight line segments.
5. For tan x, draw asymptotes at 90° and 270°; curve approaches but never touches them.
6. Label the graph and state amplitude or period if asked.

Once you have worked through a few, test yourself with the free Trigonometric Graphs quiz — it tells you fast whether the method has actually stuck.

Sin vs cos vs tan: which graph does the question want?

Students lose marks by sketching the wrong curve, omitting asymptotes on tan, or confusing sin and cos starting points. Use the equation to decide.

Graph	Key features	Typical signal words
y = sin x	Starts (0, 0); max at 90°	“sketch y = sin x”
y = cos x	Starts (0, 1); min at 180°	“sketch y = cos x”
y = tan x	Asymptotes at 90°, 270°	“sketch y = tan x”
y = a sin x	Amplitude |a|; same shape	”amplitude”, “3 sin x”

Trigonometric Graphs in past-paper wording: command words that matter

Most lost marks come from misreading the command word or plotting too few points. These are the command words you will see and what each one demands.

Command word / phrase	What the question wants	Typical stem
Sketch	Accurate shape with key points labelled	”Sketch the graph of y = sin x for 0° ≤ x ≤ 360°.”
Write down	State amplitude, period or coordinates	”Write down the amplitude of y = 2 cos x.”
Use your graph to …	Read solutions from an intersection	”Use your graph to solve sin x = 0.5.”
Draw	Neat graph on given axes	”On the grid, draw y = tan x.”
State the period	Length of one complete cycle	”Write down the period of y = sin x.”

Worked exam-style stems (how to answer the wording)

Practising the wording — not just the shapes — is what method marks reward. Here is how three real-style stems are answered.

1. “Sketch the graph of y = sin x for 0° ≤ x ≤ 360°.” Plot (0, 0), (90, 1), (180, 0), (270, −1), (360, 0); join smoothly. Mark-scheme reward: all five key points correct, smooth curve.
2. “Write down the amplitude and period of y = 4 cos x.” Amplitude = 4; period = 360°. Reward: both stated — amplitude is |4| = 4.
3. “The diagram shows y = sin x and y = 0.6. Use the graph to solve sin x = 0.6 for 0° ≤ x ≤ 360°.” Read x where the lines cross: x ≈ 37° and x ≈ 143°. Reward: both solutions in range.

When you can recognise the wording instantly, work the full set on the Trigonometry topical past paper questions and the Trigonometric Graphs quiz to lock the method in.

How Trigonometric Graphs connect to the rest of Trigonometry

Graphs link directly to Trigonometric Equations, where solutions are read from intersections, and build on Right Angled Trigonometry where sin, cos and tan values are first calculated. When you are ready to mix topics, the Cambridge IGCSE Maths resource hub lets you move straight from a weak subtopic into the next.

Common mistakes students make

• Starting cos x at 0 instead of 1.
• Drawing tan x without vertical asymptotes at 90° and 270°.
• Joining points with straight lines instead of a smooth curve.
• Confusing amplitude with period.
• Giving only one solution when sin x = k has two solutions between 0° and 360°.

When you need more support

If trigonometric graph questions keep tripping you up — especially sketching tan or reading solutions — work through the Trigonometry topical past paper questions and the Trigonometric Graphs quiz to pinpoint the exact gap, then get focused help from a Cambridge IGCSE Maths tutor to fix it quickly.

Frequently asked questions

Are trigonometric graphs hard in Cambridge IGCSE Maths? The shapes are predictable once you know the key points. Marks are lost when students confuse sin and cos starting values or omit asymptotes on tan.

What is the amplitude of y = 3 sin x? 3 — the amplitude is the coefficient of sin x (the maximum distance from the midline).

What is the period of y = sin x? 360° — one complete wave from 0° to 360°.

How do I revise Trigonometric Graphs effectively? Read the subtopic notes, plot key points on every sketch, then take the Trigonometric Graphs quiz. Revisit any tan-graph problems you got wrong before moving on.

Ready to master Cambridge IGCSE Maths Trigonometric Graphs?

Start with the Trigonometric Graphs subtopic page, then book a free trial with a Cambridge IGCSE Maths specialist to turn Trigonometric Graphs into guaranteed marks.

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