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Trigonometric Ratios Of Some Special Angles

NIOS · Class 10 · Maths

Complete topic list for Trigonometric Ratios Of Some Special Angles in NIOS Class 10 Maths. Key concepts, sub-topics, and what to focus on for board exams.

36 questions24 flashcards5 concepts

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A labeled diagram showing a right-angled isosceles triangle (angles 45°, 45°, 90°) with sides 'a' and hypotenuse 'a√2', used to derive sine, cosine, and tangent for 45 degrees.
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4 Topics · NIOS Class 10 Maths

Topics in Trigonometric Ratios Of Some Special Angles

1

1. Right-Triangle Trigonometric Ratios

  • In a right triangle, the trigonometric ratios of an acute angle are defined using the opposite side, adjacent side, and hypotenuse.
  • For an acute angle C in right triangle ABC right-angled at B: sin C = opposite/hypotenuse, cos C = adjacent/hypotenuse, tan C = opposite/adjacent.
  • The reciprocal ratios are cosec C = hypotenuse/opposite, sec C = hypotenuse/adjacent, cot C = adjacent/opposite.
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2. Values of 45°, 30°, and 60°

  • The 45° values come from an isosceles right triangle.
  • The 30° values come from an equilateral triangle split into two right triangles.
  • The 60° values come from the same equilateral-triangle construction.
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3. How the special-angle values are obtained

  • The 45° triangle is formed by taking a point on a ray making 45° with the x-axis and dropping a perpendicular to the x-axis.
  • In the 45° construction, the right triangle is isosceles, so the two legs are equal.
  • The 30° construction uses a point P, the foot M on the x-axis, and a point P prime so that triangle OPP prime becomes equilateral.
4

4. Ratios of 0° and 90°

  • Some ratios at 0° and 90° are defined, and some are not defined.
  • sin 0° = 0 and cos 0° = 1.
  • sin 90° = 1 and cos 90° = 0.

Key Concepts

Central concept: Special angle trigonometric ratios and their use in geometry and heights and distances

Basic trigonometric ratiosPythagoras theorem45 degree ratios30 degree ratios60 degree ratiosAngles 0 degree and 90 degreeMemory aid tableComplementary angle relations

Frequently Asked Questions

What are the important topics in Trigonometric Ratios Of Some Special Angles for NIOS Class 10 Maths?
Key topics in Trigonometric Ratios Of Some Special Angles include Trigonometric Ratios of Special Angles - Complete Overview, Complete Overview of Special Angles Chapter, Special Angles Trigonometric Ratios Overview. These are the concepts NIOS Class 10 examiners draw on most — study them first, then practise related questions.
How to score full marks in Trigonometric Ratios Of Some Special Angles — NIOS Class 10 Maths?
Understand the core concepts first, then work through the 36 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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