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Trigonometrical Ratios of Standard Angles

ICSE · Class 9 · Mathematics

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

34 questions32 flashcards5 concepts

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A labeled diagram showing an equilateral triangle bisected by an altitude, illustrating how to derive sine, cosine, and tangent for 30° and 60° angles using side lengths 'a' and '2a'.
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4 Topics · ICSE Class 9 Mathematics

Topics in Trigonometrical Ratios of Standard Angles

1

1. Trigonometric ratios of 30° and 60°

  • In an equilateral triangle, each angle is 60°.
  • If side BC is 2a and AD is drawn perpendicular to BC, then BD = a.
  • In right triangle ABD, AB = 2a, BD = a, and AD = √3·a.
2

2. Trigonometric ratios of 45°

  • A right-angled isosceles triangle has two equal sides AB = BC = a and one right angle of 90°.
  • The remaining two angles are 45° each.
  • Using Pythagoras theorem, AC = √2·a.
3

3. Standard-angle table and variation from 0° to 90°

  • sin 0° = 0 and cos 0° = 1.
  • sin 90° = 1 and cos 90° = 0.
  • tan 90° is not defined.
4

4. Important identities

  • The Pythagorean identity is sin²A + cos²A = 1 for any angle A.
  • The secant-tangent identity is sec²A - tan²A = 1 for any angle A.
  • The cosecant-cotangent identity is cosec²A - cot²A = 1 for any angle A.

Key Concepts

Central concept: Standard angles 0°, 30°, 45°, 60°, and 90° and their trigonometric ratios

Ratios of 30° and 60°Ratios of 45°Ratios of 0° and 90°Table of standard-angle valuesMonotonic behaviourCo-function relationshipPythagorean identitiesAddition and subtraction formulas

Frequently Asked Questions

What are the important topics in Trigonometrical Ratios of Standard Angles for ICSE Class 9 Mathematics?
Trigonometrical Ratios of Standard Angles 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 of Standard Angles — ICSE Class 9 Mathematics?
Understand the core concepts first, then work through the 34 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.

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