TEACHGYAN • CLASS 10 MATHEMATICS • NCERT 2026–27
Chapter 8: Introduction to Trigonometry
Detailed Notes • Worked Examples • Competency • Board Practice
📖 Chapter Explanation
Trigonometry describes relationships between angles and sides in right triangles. The chapter builds sine, cosine and tangent as ratios and connects them with standard angles and identities.
🧭 Concept Journey
📌 Core Concepts
For an acute angle θ in a right triangle, sinθ=opposite/hypotenuse, cosθ=adjacent/hypotenuse and tanθ=opposite/adjacent. The identity sin²θ+cos²θ=1 follows from Pythagoras.
💡 Worked Example
For an acute angle θ in a right triangle, sinθ=opposite/hypotenuse, cosθ=adjacent/hypotenuse and tanθ=opposite/adjacent. The identity sin²θ+cos²θ=1 follows from Pythagoras.
⚠️ Common Errors
For a 3-4-5 triangle with θ opposite side 3, sinθ=3/5, cosθ=4/5 and tanθ=3/4.
🧠 Concept-Based MCQs
- A wheelchair ramp forms a right triangle. Given its length and height, students calculate the angle-related ratios and explain which ratio is most direct.
Answer Key: 1-B, 2-A, 3-B, 4-B.
📊 Case-Based / Competency
Always identify the angle first. The opposite and adjacent sides change when the reference angle changes.
- Draw or identify the mathematical model.
- Select the relevant theorem/formula.
- Solve with complete working.
- Interpret and verify the answer.
🔎 Extension Case
sinθ is: A) adjacent/hypotenuse B) opposite/hypotenuse C) hypotenuse/opposite D) opposite/adjacent|tanθ equals: A) sinθ/cosθ B) cosθ/sinθ C) 1/sinθ D) 1/cosθ|sin²θ+cos²θ equals: A) 0 B) 1 C) 2 D) tanθ|At 30°, sin30° is: A) 0 B) 1/2 C) √3/2 D) 1
🔥 HOTS & Board Challenge
- Explain why the chosen method works.
- Create a similar problem and solve it.
- Find and correct a plausible incorrect solution.
- Apply the concept to a new context.
✍️ Exam Practice
- Define the central concept.
- Solve a direct application problem.
- Solve a multi-step competency problem.
- Interpret a diagram/context.
- Write a 5-mark solution with reasoning.
📄 Practice Worksheet
- 5 concept checks
- 5 standard problems
- 3 applications
- 2 case-based questions
- 2 HOTS questions
- 1 board challenge
🎯 One-Minute Revision
right triangle → opposite/adjacent/hypotenuse → sin/cos/tan → standard angles → identities → applications
🏆 Mastery Checklist
- ☐ I understand the concept.
- ☐ I can choose the correct method.
- ☐ I can solve step by step.
- ☐ I can handle competency questions.
- ☐ I can verify and interpret my answer.
← Class 10 Mathematics Free Resources | ← Class 10 Main Page
Original explanatory study material aligned to NCERT/CBSE topics; textbook passages are not reproduced verbatim.