IGCSE Trigonometric Equations: Complete Guide for Cambridge IGCSE Mathematics

IGCSE trigonometric equations are essential topics in Cambridge IGCSE Mathematics that appear in both Paper 2 and Paper 4. Mastering solving sin, cos, tan equations, finding all solutions, and trigonometric equation methods is essential for solving angle problems.

This comprehensive IGCSE trigonometric equations guide covers everything you need to know, including solving basic trigonometric equations, finding all solutions in given ranges, 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 solve trigonometric equations, find all solutions in a given range, 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 Equations Matter

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

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

Key insight from examiners: Students often forget to find all solutions or make errors with inverse trig functions. This guide will help you master these systematically.

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Understanding Trigonometric Equations

Trigonometric equations involve finding angles that satisfy equations like sin(x) = 0.5.

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Solving Basic Equations

Example 1: Solve sin(x) = 0.5 for 0° ≤ x ≤ 360°.

Solution: x = sin⁻¹(0.5) = 30° Also: x = 180° - 30° = 150° (since sin is positive in 1st and 2nd quadrants)

Answer: x = 30° or x = 150°

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Finding All Solutions

For sin(x) = k:

• Principal solution: x = sin⁻¹(k)
• Second solution: x = 180° - sin⁻¹(k)
• Add/subtract 360° for additional solutions if needed

For cos(x) = k:

• Principal solution: x = cos⁻¹(k)
• Second solution: x = 360° - cos⁻¹(k)

For tan(x) = k:

• Principal solution: x = tan⁻¹(k)
• Add 180° for second solution (tan repeats every 180°)

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Example 2: Cosine Equation

Solve cos(x) = 0.5 for 0° ≤ x ≤ 360°.

Solution: x = cos⁻¹(0.5) = 60° Also: x = 360° - 60° = 300°

Answer: x = 60° or x = 300°

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Example 3: Tangent Equation

Solve tan(x) = 1 for 0° ≤ x ≤ 360°.

Solution: x = tan⁻¹(1) = 45° Also: x = 45° + 180° = 225°

Answer: x = 45° or x = 225°

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Common Examiner Traps

• Missing solutions - Remember to find all solutions in the given range
• Quadrant errors - Know which quadrants give positive/negative values
• Range errors - Check all solutions are within the specified range

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Practice Questions

Question 1

Solve sin(x) = -0.5 for 0° ≤ x ≤ 360°.

Solution: x = sin⁻¹(-0.5) = -30° (not in range) Add 360°: x = 330° Second solution: x = 180° - (-30°) = 210°

Answer: x = 210° or x = 330°

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Tutopiya Advantage: Personalised IGCSE Trigonometric Equations Coaching

• Live whiteboard walkthroughs of trigonometric equation problems
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📞 Ready to turn shaky trigonometric equation 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 Equations

How do I solve sin(x) = k?

Find sin⁻¹(k) for principal solution, then 180° - sin⁻¹(k) for second solution (if in range).

How do I solve cos(x) = k?

Find cos⁻¹(k) for principal solution, then 360° - cos⁻¹(k) for second solution.

How do I solve tan(x) = k?

Find tan⁻¹(k) for principal solution, then add 180° for second solution.

Why are there multiple solutions?

Trigonometric functions are periodic, so equations have multiple solutions in a given range.

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Trigonometric Graphs: Complete Guide - Master trig graphs
• IGCSE Right-Angled Trigonometry: Complete Guide - Master SOHCAHTOA
• 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 Equations with Tutopiya

Ready to excel in IGCSE trigonometric equations? 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 equations and achieve your target grade.

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