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Complementary Angles

ICSE · Class 9 · Mathematics

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

41 questions28 flashcards5 concepts

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An illustration showing two acute angles whose sum is 90 degrees, defining them as complementary angles. Examples like 30 and 60 degrees, and a general case with x and (90-x) degrees.
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4 Topics · ICSE Class 9 Mathematics

Topics in Complementary Angles

1

1. Core idea of complementary angles

  • Two acute angles are complementary only if their sum equals 90°.
  • 30° and 60° are complementary because 30° + 60° = 90°.
  • 70° and 20° are complementary because 70° + 20° = 90°.
2

2. Sine and cosine complementary identities

  • In a right triangle ABC with ∠B = 90°, if ∠ACB = θ, then ∠CAB = 90°−θ.
  • sin θ = cos(90°−θ).
  • cos(90°−θ) = sin θ.
3

3. Tangent and cotangent complementary identities

  • tan(90°−θ) = cot θ.
  • cot(90°−θ) = tan θ.
  • In the right triangle proof, tan uses perpendicular/base and cot uses base/perpendicular.
4

4. Secant and cosecant complementary identities

  • cosec(90°−θ) = sec θ.
  • sec(90°−θ) = cosec θ.
  • cosec θ is defined as hypotenuse divided by perpendicular.

Key Concepts

Central concept: Complementary angles and their trigonometric co-function identities

Complementary anglesRight triangle ABCSine and cosine identitiesTangent and cotangent identitiesSecant and cosecant identitiesTriangle angle sumWorked examples and evaluation

Frequently Asked Questions

What are the important topics in Complementary Angles for ICSE Class 9 Mathematics?
Complementary 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 Complementary Angles — ICSE Class 9 Mathematics?
Understand the core concepts first, then work through the 41 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 Complementary Angles

All 28 chapters — ICSE Class 9 Mathematics Syllabus

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