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Syllabus

Complementary Angles — Syllabus

ICSE · Class 9 · Mathematics

What Complementary Angles covers in ICSE Class 9 Mathematics: 4 topics, for the 2026-27 session. Part of the ICSE Class 9 Mathematics syllabus.

41 questions28 flashcards18 formulas & key relations5 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 · 2026-27

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

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Frequently Asked Questions

What are the important topics in Complementary Angles for ICSE Class 9 Mathematics?
Key topics in Complementary Angles include Core idea of complementary angles, Sine and cosine complementary identities, Tangent and cotangent complementary identities, Secant and cosecant complementary identities. Study these first, then practise questions on each for Class 9 exams.
How should I revise Complementary Angles for Class 9 exams?
Learn the core ideas first, then work through the 41 practice questions on Complementary Angles. 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 Syllabus

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