Chapter 7 Topics – Trigonometry
Click on any topic to expand and view its exercises. Each section includes step-by-step solutions and real-world applications.
7.1 – Trigonometric Ratios & Extending Angles
Ratios, special angles, signs, angles between 90° and 180°
New 2026
This section introduces the six trigonometric ratios, their values for special angles (0°, 30°, 45°, 60°, 90°, 180°), signs in different quadrants, and extends sine and cosine functions to angles between 90° and 180° using the unit circle.
7.1
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Exercise 7.1
Ratios, signs & extended angles
7.2 – Laws of Sines, Cosines & Area
Oblique triangles, law of sines, law of cosines, area formulas
New 2026
This section covers the law of sines, law of cosines, and area formulas for any triangle (oblique triangles). You'll learn to solve triangles when given different combinations of sides and angles, and calculate areas using various methods.
7.2
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Exercise 7.2
Law of sines, cosines, area
7.3 – 3D Trigonometry & Real-World Applications
Three-dimensional problems, prisms, pyramids, cuboids
New 2026
This section applies trigonometry to three-dimensional problems involving prisms, pyramids, cuboids, and other 3D shapes. You'll calculate lengths, angles between lines and planes, and solve real-world problems in architecture and engineering.
7.3
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Exercise 7.3
3D problems, prisms, pyramids
7.4 – Three-Figure Bearings & Navigation
Bearings, navigation, real-world problems
New 2026
This section covers three-figure bearings, their interpretation, and applications in navigation, aviation, and surveying. You'll learn to find bearings between points, calculate distances, and solve real-world navigation problems.
7.4
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Exercise 7.4
Bearings & navigation
Review Exercise 7
Complete revision and mixed practice problems
New 2026
The review exercise mixes questions from all four sections of Chapter 7, giving you a chance to test whether you can move between topics without a hint about which method applies — a useful checkpoint before exams.
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Review Exercise 7
Complete Revision & Practice
Trigonometry – What's Inside This Chapter (PECTAA 2026)
Chapter 7 – Trigonometry is part of Class 10 Mathematics under the Revised National Curriculum 2023. Trigonometry has applications in architecture, navigation, and wave phenomena. This unit covers trigonometric identities, equations, inverse functions, and real-world problem solving for height and distance calculations, wave analysis, and engineering design.
Prepared by Muhammad Tayyab, Govt Christian High School Daska, this chapter's notes cover all 4 exercises plus the review exercise, with step-by-step solutions throughout.
✅ What This Chapter Covers
- ✓Trigonometric identities, equations, inverse functions, real-world applications
- ✓Step-by-step solved exercises for all 4 sections
- ✓Based on the PECTAA 2026 syllabus
- ✓A complete review exercise for revision
- ✓Free access, no downloads required
🌐 Why This Chapter Matters
Trigonometry has applications in architecture, navigation, and wave phenomena. This unit covers trigonometric identities, equations, inverse functions, and real-world problem solving for height and distance calculations, wave analysis, and engineering design.
Mastering this chapter builds a foundation for higher studies and board exam success under the PECTAA 2026 syllabus.
Browse Notes by Individual Chapter
Each chapter also has its own dedicated page with exercise cards and full notes.
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Chapter 1: Complex Numbers
Complex number operations, Argand diagrams, and engineering applications with step-by-step solved exercises.
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Chapter 2: Quadratic Equations and Inequalities
Solving techniques, discriminant analysis, optimization applications, and real-world problem solving strategies.
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Chapter 3: Matrices and Determinants
Matrix operations, determinants, inverses, and computer graphics applications with complete solved exercises.
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Chapter 4: Functions and Graphs
Function types, properties, graphing techniques, and scientific applications for comprehensive understanding.
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Chapter 5: Algebraic Fractions
Simplification, operations, solving equations, and engineering applications with detailed step-by-step solutions.
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Chapter 6: Vectors in Plane
Vector operations, dot product, and physics and engineering applications with practical solved problems.
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Chapter 7: Trigonometry
Trigonometric identities, equations, inverse functions, and real-world applications in architecture and navigation.
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Chapter 8: Chords and Arcs of a Circle
Relationships between chords, arcs, angles, and design and engineering applications for circular geometry.
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Chapter 9: Tangent and Angles of a Circle
Tangent properties, angle relationships, and geometry and design applications with construction techniques.
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Chapter 10: Practical Geometry of Circles
Geometric constructions, tangents, inscribed figures, and step-by-step methods for technical drawing.
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Chapter 11: Information Handling
Data collection, graphical representations, statistical analysis, and decision making for real-world problems.
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Chapter 12: Probability
Basic concepts, compound events, conditional probability, and real-world applications in risk assessment.
Explore the Complete Class 10 Math Toolkit
This chapter page is part of the full Class 10 Math resource set. Dive deeper into any subject-wide resource below.
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Class 10 Math Notes Hub
The main hub linking every Class 10 Math chapter in one place.
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Math Key Book
Full solution guide with chapter-wise answers to every textbook question.
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Notes PDF
Downloadable and printable chapter-wise PDF notes for offline study.
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Solved Exercises
Step-by-step worked solutions for every exercise in all 12 chapters.
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Important Questions
Short and long board-focused questions to prioritize your revision.
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Math MCQs
Chapter-wise multiple-choice questions with an online practice test.
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Definitions
Every key term and theorem explained clearly, chapter by chapter.
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Formula Sheet
A quick-revision sheet with all formulas organized by chapter.
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Guess Paper
The latest important chapters and exercises predicted for this year's exam.
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Past Papers
Solved previous board papers with pattern analysis for smarter prep.