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Complementary Angles — Chapter Summary

ICSE · Class 9 · Mathematics

Summary of Complementary Angles for ICSE Class 9 Mathematics. Key concepts: Two acute angles are, The complement of an acute and sin(90° − θ) = cos θ.

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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Overview

Complementary angles are two acute angles whose sum is 90°. The complement of an angle θ is (90 − θ)°. In a right triangle, the two acute angles are complementary, and this idea creates the co-function relations between trigonometric ratios. These relations make it possible to replace one trigonomet

Key Concepts

Two acute angles are complementary if

Two acute angles are complementary if their sum is 90°. Examples include 30° and 60°, 70° and 20°, and x° and (90 − x)°.

The complement of an acute angle

The complement of an acute angle θ is (90 − θ)°. For example, the complement of 48° is 42°.

sin(90° − θ) = cos θ

sin(90° − θ) = cos θ and cos(90° − θ) = sin θ. In right triangle ABC with ∠B = 90° and ∠ACB = θ, the angle ∠CAB is 90° − θ, which leads to this identi

tan(90° − θ) = cot θ

tan(90° − θ) = cot θ and cot(90° − θ) = tan θ.

cosec(90° − θ) = sec θ

cosec(90° − θ) = sec θ and sec(90° − θ) = cosec θ.

Learning Objectives

  • Define complementary angles correctly.
  • Find the complement of a given acute angle.
  • Use the right triangle model to connect complementary angles with trigonometric ratios.
  • Apply the complementary identities for sine, cosine, tangent, cotangent, secant, and cosecant.
  • Solve and verify trigonometric expressions using complementary angle relations.

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 Chapter Summary

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