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Formula Sheet

Complementary Angles — Formula Sheet

ICSE · Class 9 · Mathematics

18 formulas from Complementary Angles (ICSE Class 9 Mathematics) on one page, grouped by topic. 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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18 Entries · 7 Sections

Formulas and Key Relations

Core Definitions

Complement of θ° = (90 − θ)°

sin(90° − θ) = cos θ

cos(90° − θ) = sin θ

tan(90° − θ) = cot θ

cot(90° − θ) = tan θ

Triangle-Based Trigonometric Relations

sin θ = AB/AC

cos(90° − θ) = AB/AC

tan θ = AB/BC

cot(90° − θ) = AB/BC

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.

Tangent and cotangent complementary identities

tan(90°−θ) = cot θ.

cot(90°−θ) = tan θ.

Secant and cosecant complementary identities

cosec(90°−θ) = sec θ.

sec(90°−θ) = cosec θ.

In triangle ABC with ∠B = 90° and ∠ACB = θ, ∠CAB = 90° − θ.

Key relations

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

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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 many formulas are in Complementary Angles?
This sheet lists 18 formulas from Complementary Angles, grouped by topic. Learn what each symbol stands for so you can apply the formula, not just recall it.
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 Formula Sheet

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