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Formula Sheet

Trigonometrical Ratios of Standard Angles

ICSE · Class 9 · Mathematics

All formulas from Trigonometrical Ratios of Standard Angles in ICSE Class 9 Mathematics. Key equations, constants, and identities for board exam preparation.

34 questions32 flashcards5 concepts

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A labeled diagram showing an equilateral triangle bisected by an altitude, illustrating how to derive sine, cosine, and tangent for 30° and 60° angles using side lengths 'a' and '2a'.
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20 Formulas · 4 Sections

Formulas

1. Standard Angles and Right-Triangle Results

sin 30° = 1/2

cos 60° = 1/2

tan 60° = √3

sin 0° = 0 and cos 0° = 1

sin 90° = 1 and cos 90° = 0

2. Exact Trigonometric Ratios of Standard Angles

sin 30° = 1/2, cos 30° = √3/2, tan 30° = 1/√3

sin 45° = 1/√2, cos 45° = 1/√2, tan 45° = 1

sin 60° = √3/2, cos 60° = 1/2, tan 60° = √3

cot 30° = √3, sec 30° = 2/√3, cosec 30° = 2

cot 45° = 1, sec 45° = √2, cosec 45° = √2

3. Co-Function and Identity Rules

If x = y = 45° or x + y = 90°, then sin x = cos y

If x = y = 45° or x + y = 90°, then tan x = cot y

If x = y = 45° or x + y = 90°, then sec x = cosec y

sin 45° = cos 45° = 1/√2

sin 30° = cos 60° = 1/2

4. Solving Trigonometric Equations

If sin 2A = 1, then 2A = 90°

If cos 3A = 1/2, then 3A = 60°

If tan 3A = 1, then 3A = 45°

If 4sin²x° - 3 = 0, then sin x° = √3/2

For acute x, 4sin²x° - 3 = 0 gives x = 60°

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Frequently Asked Questions

What are the important topics in Trigonometrical Ratios of Standard Angles for ICSE Class 9 Mathematics?
Trigonometrical Ratios of Standard 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 Trigonometrical Ratios of Standard Angles — ICSE Class 9 Mathematics?
Understand the core concepts first, then work through the 34 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.

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