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Revision Notes

Trigonometrical Ratios — Revision Notes

ICSE · Class 9 · Mathematics

Trigonometrical Ratios revision notes for ICSE Class 9 Mathematics: 4 topics in quick points. Part of the ICSE Class 9 Mathematics syllabus.

36 questions26 flashcards16 formulas & key relations5 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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Key Topics to Revise

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.

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Full Notes

Key Concepts

Trigonometry means measurement of trianglesFor a chosen acute angleThe six ratios are sineThe names perpendicular and base changeEach trigonometric ratio is a real

Frequently Asked Questions

What are the important topics in Trigonometrical Ratios for ICSE Class 9 Mathematics?
Key topics in Trigonometrical Ratios include Basic Ideas in a Right Triangle, Six Trigonometrical Ratios, Worked Calculations and Standard Results, Geometry-Based Applications. Study these first, then practise questions on each for Class 9 exams.
How should I revise Trigonometrical Ratios for Class 9 exams?
Learn the core ideas first, then work through the 36 practice questions on Trigonometrical Ratios. Revise 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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All ICSE Class 9 Mathematics Revision Notes

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