- 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.
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.
