Revision Notes Class 10 Maths Chapter 8 – Introduction to Trigonometry

• Ratio definitions (right triangle, angle θ): sinθ=opp/hyp, cosθ=adj/hyp, tanθ=opp/adj=sinθ/cosθ.
• Reciprocals: cosecθ=1/sinθ, secθ=1/cosθ, cotθ=1/tanθ=cosθ/sinθ.
• Standard angle values: sin: 0, 1/2, 1/√2, √3/2, 1 (for 0°,30°,45°,60°,90°); cos is the reverse order; tan: 0, 1/√3, 1, √3, undefined.
• Pythagorean identities: sin²θ+cos²θ=1; 1+tan²θ=sec²θ; 1+cot²θ=cosec²θ.
• Complementary angle rules (A+B=90°): sin(90°−θ)=cosθ, cos(90°−θ)=sinθ, tan(90°−θ)=cotθ, cot(90°−θ)=tanθ, sec(90°−θ)=cosecθ, cosec(90°−θ)=secθ.
• Undefined cases: tanθ and secθ undefined at 90°; cotθ and cosecθ undefined at 0°.
• Behaviour 0°→90°: sinθ and tanθ increase; cosθ and cotθ decrease; secθ increases, cosecθ decreases.
• Common trap: trigonometric ratios are never treated as ordinary algebraic products — “sin A” is one symbol, not sin × A.

Part of the Class 10 Maths Chapter 8 cluster: Solutions | Extra Questions (HOTS) | Revision Notes | Formulas Handbook | Class 10 Maths book page. These Class 10 Mathematics Chapter 8 notes are ideal for quick revision just before exams.

Last Updated: October 24, 2026

Why This Chapter Matters

Introduction to Trigonometry is one of the standard chapters in the CBSE/NCERT Class 10 Maths syllabus and questions from it appear regularly in board exams, in formats ranging from 1-mark objective questions to longer 3-5 mark descriptive or numerical questions. Because the concepts here often build on earlier chapters (and feed into later ones), a solid grip on this chapter also makes the rest of the Maths syllabus easier to follow.

How to Use These Notes

These revision notes are meant for quick recall in the last few days before an exam or unit test — they are not a substitute for first reading the full chapter and working through examples in the NCERT textbook. A good routine is: read the chapter once, solve the in-text and end-of-chapter questions using the linked Solutions, then come back to this page a day or two before the exam to refresh the key definitions and formulas without re-reading the whole chapter.

Common Mistakes to Avoid

Students often mix up which side is “opposite” and which is “adjacent” when the angle changes position in a right triangle — always identify the angle first, then label the sides relative to it. Another frequent error is forgetting that trigonometric ratios are defined only for right-angled triangles, and applying formulas meant for angles between 0° and 90° to obtuse angles without adjustment. Practising with a variety of triangle orientations, not just the standard textbook diagram, builds the flexibility needed for exam questions.

Frequently Asked Questions

Why are the trigonometric ratios defined only for right triangles?
Because the ratios (sine, cosine, tangent etc.) are defined specifically in terms of the sides relative to a right angle — the hypotenuse, the side opposite the angle, and the side adjacent to it — which only has a fixed, unambiguous meaning in a right-angled triangle.

How are the trigonometric ratios of complementary angles related?
sin(90-theta) = cos(theta), and similarly tan(90-theta) = cot(theta), sec(90-theta) = cosec(theta) — each ratio of an angle equals the co-ratio of its complement, a relationship used often to simplify trigonometric expressions.

What to Revise First (and Last) in This Chapter

Written by Satish

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