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Revision Notes

Complementary Angles — Revision Notes

ICSE · Class 9 · Mathematics

Complementary Angles revision notes for ICSE Class 9 Mathematics: 4 topics in quick points. 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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Key Topics to Revise

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.

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Full Notes

Key Concepts

Two acute angles are complementary ifThe complement of an acute anglesin(90° − θ) = cos θtan(90° − θ) = cot θcosec(90° − θ) = sec θ

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.

More resources for Complementary Angles

All ICSE Class 9 Mathematics Revision Notes

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