Who this is for: Cambridge IGCSE Mathematics (0580/0607) students who want Trigonometric Graphs — sketching and reading sin, cos and tan curves, and understanding amplitude and period — to become a reliable source of marks instead of a topic they only half-remember.
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 bridge ratio work and equation-solving in Cambridge IGCSE Mathematics (0580/0607). Examiners expect you to sketch y = sin x, y = cos x and y = tan x for 0° ≤ x ≤ 360°, read solutions from graphs, and recognise how changes to the equation affect amplitude and period. This guide explains exactly what the subtopic covers, how to handle the question types that actually appear, and where to practise each skill.

Key takeaways

• y = sin x and y = cos x have amplitude 1, period 360°, and oscillate between −1 and 1.
• y = tan x has period 180° and undefined values at 90° and 270° (vertical asymptotes).
• y = a sin x has amplitude |a|; y = sin(bx) has period 360°/b.
• sin x starts at 0; cos x starts at 1 — use these anchors when sketching from 0° to 360°.

What are Trigonometric Graphs in Cambridge IGCSE Maths?

Trigonometric Graphs show how sin, cos and tan ratios change as the angle increases. On Cambridge IGCSE Mathematics papers you sketch curves, read off how many solutions an equation has in a given range, and interpret transformations such as y = 2 sin x or y = sin 2x. This subtopic prepares you for Trigonometric Equations, where graphs justify the number of solutions.

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
Basic sin/cos shape	Wave between −1 and 1	”Sketch y = sin x for 0° ≤ x ≤ 360°“
tan graph	Period 180°, asymptotes at 90°, 270°	“Sketch y = tan x”
Amplitude	Vertical stretch: y = a sin x	”Write down the amplitude of y = 3 cos x”
Period	Horizontal compression: y = sin(bx)	“Write down the period of y = sin 2x”

How to sketch trigonometric graphs — step by step

The safest method works for every graph question in this subtopic.

1. State the range of x (usually 0° to 360°).
2. Plot key points — for sin/cos: 0°, 90°, 180°, 270°, 360°.
3. Mark amplitude — maximum and minimum y-values.
4. For tan, plot at 0°, 45°, 90° (asymptote), 135°, 180°, etc.
5. Join smoothly — sin and cos as waves; tan in separate branches.
6. Label axes and indicate asymptotes with dashed lines for tan.

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, cos or tan: which graph does the question want?

Students lose marks by sketching the wrong curve or missing asymptotes on tan. Use the equation to decide.

Graph	Key features	Typical signal
y = sin x	Starts (0,0); max at 90°; min at 270°	“sin x”, “sine graph”
y = cos x	Starts (0,1); min at 180°	“cos x”, “cosine graph”
y = tan x	Asymptotes at 90°, 270°; period 180°	“tan x”, “tangent graph”
y = a sin x + k	Amplitude |a|; vertical shift k	”Write the amplitude and period”

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

Most lost marks come from wrong key points or incorrect period. 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.”
Write down the amplitude	|a| in y = a sin x	”Write down the amplitude of y = −2 cos x.”
Write down the period	360°/b for y = sin(bx)	“Find the period of y = cos 3x.”
How many solutions	Count intersections with a horizontal line	”How many solutions does sin x = 0.5 have for 0° ≤ x ≤ 360°?”
Solve by graph	Read x-values from a sketch or given graph	”Use your graph to solve cos x = −0.5.”

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°.” Key points: (0,0), (90,1), (180,0), (270,−1), (360,0). Smooth wave through them. Mark-scheme reward: correct coordinates at multiples of 90°.
2. “Write down the amplitude and period of y = 3 sin 2x.” Amplitude = 3; period = 360°/2 = 180°. Reward: both stated clearly.
3. “For 0° ≤ x ≤ 360°, write down the number of solutions of the equation sin x = 0.6.” Horizontal line y = 0.6 crosses y = sin x twice → 2 solutions. Reward: reference to symmetry of sin graph.

When you can recognise the wording instantly, move on to Trigonometric Equations and take the Trigonometric Graphs quiz to lock the method in.

How Trigonometric Graphs connect to the rest of Trigonometry

Graphs justify solutions in Trigonometric Equations. They build on ratio values from Right Angled Trigonometry and link to Graphs of Functions for transformations. The Cambridge IGCSE Maths resource hub links all subtopics.

Common mistakes students make

• Sketching cos x starting at 0 like sin x.
• Forgetting asymptotes on y = tan x at 90° and 270°.
• Confusing amplitude with period.
• Using radian scale when the question specifies degrees.
• Drawing sin/cos below −1 or above 1 when there is no vertical stretch.

When you need more support

If graph sketches or period questions keep tripping you up, work through 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 basic shapes are predictable — marks are lost on wrong key points, tan asymptotes and mixing up amplitude with period.

What is the period of y = sin x? 360° — the graph repeats every full turn.

How is y = tan x different from sin and cos? Tan has vertical asymptotes where cos x = 0 (at 90° and 270°) and repeats every 180°.

How do I revise Trigonometric Graphs effectively? Read the subtopic notes, sketch all three graphs from memory with key points, then take the Trigonometric Graphs quiz. Practise counting solutions for equations like sin x = k.

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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