IGCSE Trigonometric Graphs: Complete Guide for Cambridge IGCSE Mathematics

IGCSE trigonometric graphs are essential topics in Cambridge IGCSE Mathematics that appear in both Paper 2 and Paper 4. Mastering sine, cosine, and tangent graphs, graph transformations, and period and amplitude is essential for understanding trigonometric functions.

This comprehensive IGCSE trigonometric graphs guide covers everything you need to know, including drawing sine, cosine, and tangent graphs, understanding transformations, worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to draw trigonometric graphs, identify key features, apply transformations, and apply these skills to solve problems in IGCSE exams.

Already studying with Tutopiya? Practice these skills with our dedicated IGCSE Trigonometry practice deck featuring exam-style questions and instant feedback.

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Why IGCSE Trigonometric Graphs Matter

IGCSE trigonometric graphs are essential topics. Here’s why they’re so important:

• High frequency topic: Trigonometric graph questions appear regularly in IGCSE maths papers
• Foundation skill: Essential for understanding trigonometric functions
• Exam weight: Typically worth 5-8 marks per paper
• Real-world applications: Used in physics, engineering, and wave analysis
• Problem-solving skills: Develops graph interpretation and transformation abilities

Key insight from examiners: Students often struggle with graph transformations or identifying key points. This guide will help you master these systematically.

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Understanding Trigonometric Graphs

Trigonometric graphs show how sine, cosine, and tangent values change with angle.

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Sine Graph (y = sin x)

Key features:

• Period: 360° (repeats every 360°)
• Range: -1 to 1
• Passes through (0, 0)
• Maximum at 90°: y = 1
• Minimum at 270°: y = -1

Shape: S-shaped wave starting at origin

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Cosine Graph (y = cos x)

Key features:

• Period: 360°
• Range: -1 to 1
• Passes through (0, 1)
• Maximum at 0° and 360°: y = 1
• Minimum at 180°: y = -1

Shape: Wave starting at maximum

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Tangent Graph (y = tan x)

Key features:

• Period: 180° (repeats every 180°)
• Range: All real numbers
• Asymptotes at 90°, 270°, etc.
• Passes through (0, 0)

Shape: Repeated curves with vertical asymptotes

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Graph Transformations

y = sin(x + k): Horizontal translation y = sin(x) + k: Vertical translation y = a sin(x): Vertical stretch (amplitude = a) y = sin(bx): Horizontal stretch (period = 360°/b)

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Common Examiner Traps

• Period confusion - Sine/cosine: 360°, Tangent: 180°
• Amplitude errors - Amplitude is distance from center to peak
• Transformation errors - Check direction and scale of transformations

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Practice Questions

Question 1

Sketch y = 2 sin(x) for 0° ≤ x ≤ 360°.

Solution: Amplitude = 2 (instead of 1) Graph oscillates between -2 and 2

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Tutopiya Advantage: Personalised IGCSE Trigonometric Graphs Coaching

• Live whiteboard walkthroughs of trigonometric graph problems
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📞 Ready to turn shaky trigonometric graph skills into exam-ready confidence? Book a free IGCSE maths trial and accelerate your revision plan.

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Frequently Asked Questions About IGCSE Trigonometric Graphs

What is the period of sine and cosine graphs?

The period is 360° - the graph repeats every 360°.

What is the period of tangent graph?

The period is 180° - the graph repeats every 180°.

What is amplitude?

Amplitude is the maximum distance from the center line to the peak (for sine and cosine).

How do transformations affect graphs?

• +k inside: Horizontal shift
• +k outside: Vertical shift
• ×a: Vertical stretch (amplitude)
• ×b inside: Horizontal stretch (period)

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Trigonometric Equations: Complete Guide - Master solving trig equations
• IGCSE Graphs of Functions: Complete Guide - Master function graphs
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

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Next Steps: Master IGCSE Trigonometric Graphs with Tutopiya

Ready to excel in IGCSE trigonometric graphs? Our expert IGCSE maths tutors provide:

• Personalized 1-on-1 tutoring tailored to your learning pace
• Exam-focused practice with real Cambridge IGCSE past papers
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• Flexible scheduling to fit your revision timetable

Book a free IGCSE maths trial lesson and get personalized support to master trigonometric graphs and achieve your target grade.

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