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°
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.
Ratios, signs & extended angles
7.2 – Laws of Sines, Cosines & Area
Oblique triangles, law of sines, law of cosines, area formulas
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.
Law of sines, cosines, area
7.3 – 3D Trigonometry & Real-World Applications
Three-dimensional problems, prisms, pyramids, cuboids
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.
3D problems, prisms, pyramids
7.4 – Three-Figure Bearings & Navigation
Bearings, navigation, real-world problems
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.
Bearings & navigation
Review Exercise 7
Complete revision and mixed practice problems
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.
Complete Revision & Practice
Trigonometry – What's Inside This Chapter
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 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.
Related Chapter 7 Resources
📖 Definitions
Key terms and theorems for Chapter 7.
🧮 Formula Sheet
Trigonometric formulas at a glance.
✅ Chapter MCQs
Practice multiple choice questions.
🎯 Guess Paper
Important questions predicted for exams.
🗂️ Past Papers
Solved previous board papers.
📔 Math Key Book
Full solution guide for all chapters.