Introduction to Trigonometry | CBSE Class 10 Revision & Important Questions

Introduction to Trigonometry Class 10 – Continuing our series for Class 10 Revision for CBSE board exams, we bring you a new chapter today i.e. Introduction to Trigonometry

Concepts to be covered in this article are:

  1. Trigonometric Ratios
  2. Values of Trigonometric Ratios for angles 0°,30°,45°,60° and 90°.
  3. Trigonometric Ratios of Complementary Angles
  4. Trigonometric Identities

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Let’s discuss each topic of Introduction to Trigonometry one-by-one

Trigonometric Ratios

Trigonometric Ratios are defined for the ratio of sides of any right triangle. We know that, a right triangle has 3 sides. We can obtain 6 different ratios using these side and each of these ratios has a specific name, for example,

introduction to trigonometry

Values of Trigonometric Ratios for angles 0°,30°,45°,60° and 90°

The standard angles for which we study values of trigonometric ratios are 0°,30°,45°,60° and 90°. These values will help you solve questions from this chapter as well as the next chapter that is applications of trigonometry.

introduction to trigonometry

Note that:

  • The values for sec 90°, cosec 0°, tan 90° and cot 0° are not defined.
  • The value of sin? or cos? never exceeds 1, whereas the value of sec? or cosec? is always greater than or equal to 1.
  • These values can be derived geometrically and its derivation can be asked in boards.

Trigonometric Ratios of Complementary Angles:

Two angles are said to be complementary if their sum is equal to 90°. The relationship between the value of trigonometric ratios of complementary angles is as follows:
sin (90° – ?) = cos ?
cos (90° – ?) = sin ?
tan (90° – ?) = cot ?
cot (90° – ?) = tan ?
sec (90° – ?) = cosec ?
cosec (90° – ?) = sec ?

Note: This is defined for all values of ? when 0°<?<90°. But when ? = 0° or 90°, we need to check if the values are defined for a particular ratio or not. For example: tan90° is not defined.

Trigonometric Identities

There are 3 basic trigonometric identities which can be listed as:

  • sin2?+cos2?=1, for all values of ?
  • sec2?−tan2?=1, for 0°≤?<90°
  • cosec2?=1+cot2?, for 0°<?≤90°

Lets solve a question based on these concepts:

Q. Evaluate

introduction to trigonometry

Download Previous Year’s Questions Here

Let’s solve one of the questions:

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