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Trigonometric Ratios Of Some Special Angles — Revision Notes

NIOS · Class 10 · Maths

Trigonometric Ratios Of Some Special Angles revision notes for NIOS Class 10 Maths: 4 topics in quick points. Part of the NIOS Class 10 Maths syllabus.

36 questions24 flashcards18 formulas & key relations5 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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Key Topics to Revise

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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.
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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.

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Full Notes

Key Concepts

For an acute angle CIn a right triangle ABC rightIn the 45° constructionIn the 30° constructionIn the 60° construction

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 Right-Triangle Trigonometric Ratios, Values of 45°, 30°, and 60°, How the special-angle values are obtained, Ratios of 0° and 90°. Study these first, then practise questions on each for the NIOS Class 10 board exam.
How should I revise Trigonometric Ratios Of Some Special Angles for the NIOS Class 10 board exam?
Learn the core ideas first, then work through the 36 practice questions on Trigonometric Ratios Of Some Special 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.

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