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Trigonometrical Ratios

ICSE · Class 9 · Mathematics

Complete topic list for Trigonometrical Ratios in ICSE Class 9 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

36 questions26 flashcards5 concepts

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A right-angled triangle with one acute angle labeled as the angle of reference. The sides opposite to the acute angle, adjacent to the acute angle, and opposite to the right angle are clearly labeled
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4 Topics · ICSE Class 9 Mathematics

Topics in Trigonometrical Ratios

1

1. Basic Ideas in a Right Triangle

  • The side opposite to the acute angle is the perpendicular.
  • The side adjacent to the acute angle is the base.
  • The side opposite to the right angle is the hypotenuse.
2

2. Six Trigonometrical Ratios

  • The six trigonometrical ratios are sin, cos, tan, cot, sec, and cosec.
  • Each ratio is a real number and has no unit.
  • For angle A in triangle ABC, the standard ratios are written using BC, AB, and AC.
3

3. Worked Calculations and Standard Results

  • When AC = 13 and AB = 5 in a right triangle, BC = 12 using Pythagoras theorem.
  • For that triangle, sin A = 12/13, cos C = 12/13, tan A = 12/5, and cosec C = 13/5.
  • For the same triangle, sec^2 A - tan^2 A = 1.
4

4. Geometry-Based Applications

  • In a triangle ABC with AP perpendicular to BC, if cot B = 4/3 and cot C = 12/5, then AP = 30 cm when BC = 112 cm.
  • In a rhombus ABCD with AC = 18 cm, OA = OC = 9 cm because diagonals of a rhombus bisect each other.
  • In a rhombus, diagonals bisect each other at right angle.

Key Concepts

Central concept: Trigonometry in right-angled triangles

Right-angled triangleAngle of referenceSix trigonometric ratiosReciprocal relationsQuotient relationsPythagoras theoremWorked examplesIdentities and expressions

Frequently Asked Questions

What are the important topics in Trigonometrical Ratios for ICSE Class 9 Mathematics?
Trigonometrical Ratios covers several key topics that are frequently asked in ICSE Class 9 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Trigonometrical Ratios — ICSE Class 9 Mathematics?
Understand the core concepts first, then work through the 36 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Trigonometrical Ratios

All 28 chapters — ICSE Class 9 Mathematics Syllabus

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