Trigonometry Class 10 Complete Guide with Formulas Values and Solved Problems

Jul 13, 2026

153

A Class 10 trigonometry guide covering right-triangle concepts, six trigonometric ratios, relations among them, standard-angle values, and key identities. Includes step-by-step solved problems for finding sides/angles, using identities to derive values, and application questions on height and distance using angle of elevation. Ends with revision practice questions and solving tips.

LanguageEnglish

CategoryExam

FormatPDF

Pages5

Reading Time13 min

AccessFree to download

Trigonometry Class ×Ö: Complete Guide with Formulas, Values & Solved Problems From: [https://www.youtube.com/watch?v=PUB](https://www.youtube.com/watch?v=PUB)ÖTaZÝbhA Trigonometry is one of the most scoring and fundamental chapters in Class ×Ö Mathematics. It focuses on the relationships between the angles and sides of rightangled triangles, with real-life uses in finding heights and distances of objects we cannot measure directly. This guide covers all core concepts, must-learn formulas, trigonometric values for standard angles, identities, and step-by-step solved problems to help you understand and practice effectively for exams. What is Trigonometry? Trigonometry is the branch of mathematics that deals with the ratios of sides of a rightangled triangle with respect to its acute angles. For Class ×Ö, we only study trigonometry for right triangles and acute angles (Ö° to ßÖ°) . The main goal is to use these ratios to find unknown sides or angles and solve real-world height and distance problems. Trigonometric Ratios in a Right-Angled Triangle Consider a right-angled triangle ABC, right-angled at B. For acute angle ∠A: • Opposite side (perpendicular): BC • Adjacent side (base): AB • Hypotenuse: AC (longest side, opposite the right angle) The six trigonometric ratios are defined as: × . sine (sin) A = Opposite / Hypotenuse = BC / AC Ø . cosine (cos) A = Adjacent / Hypotenuse = AB / AC Ù . tangent (tan) A = Opposite / Adjacent = BC / AB Ú . cosecant (cosec) A = Hypotenuse / Opposite = ×/sin A Û . secant (sec) A = Hypotenuse / Adjacent = ×/cos A Ü . cotangent (cot) A = Adjacent / Opposite = ×/tan A Simple shortcut: sin = Opp/Hyp, cos = Adj/Hyp, tan = Opp/Adj Relation Between Trigonometric Ratios • tan θ = sin θ / cos θ • cot θ = cos θ / sin θ • cosec θ = × / sin θ • sec θ = × / cos θ • cot θ = × / tan θ Trigonometric Ratios of Standard Angles (Ö° , ÙÖ° , ÚÛ° , ÜÖ° ,ßÖ° ) This table is essential for solving all Class ×Ö trigonometry questions quickly. | Angle | sin θ | cos θ | tan θ | cosec θ | sec θ | | --- | --- | --- | --- | --- | --- | | Ö° | Ö | × | Ö | Not defined | × | | ÙÖ° | ×/Ø | √3/2 | 1/√3 | Ø | 2/√3 | | ÚÛ° | 1/√2 | 1/√2 | × | √2 | √2 | | ÜÖ° | √3/2 | ×/Ø | √3 | 2/√3 | Ø | | ßÖ° | × | Ö | Not defined | × | Not defined | Trigonometric Identities for Class ×Ö These three identities are used to simplify expressions and prove equations in exams: × . sin² θ + cos² θ = ×Ø . × + tan² θ = sec² θÙ . × + cot² θ = cosec² θ These identities help convert one ratio into another and solve complex trigonometric equations easily. Solved Example ×: Finding Trigonometric Ratios Question: In triangle ABC, right-angled at B, AB = ØÚ cm, BC = Ý cm. Find s in A, cos A, sin C, cos C. Solution: Step × : Find hypotenuse AC using Pythagoras theorem AC² = AB² + BC² = ØÚ² + Ý² = ÛÝÜ + Úß = ÜØÛ AC = √ÜØÛ = ØÛ cm Step Ø: For ∠A Opposite = BC = Ý cm, Adjacent = AB = ØÚ cm, Hypotenuse = ØÛ cm sin A = Opp/

Jul 13, 2026

153

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