NCERT CBSE Class 10th Mathematics Chapter 8: Introduction to Trigonometry

Safalta Expert Published by: Sylvester Updated Wed, 22 Jun 2022 06:47 PM IST

Highlights

NCERT CBSE Class 10th Mathematics Chapter 8: Introduction to Trigonometry

The eighth chapter in Mathematics textbook is 'Introduction to Trigonometry'.
  • Position of a point P in the Cartesian plane with respect to co-ordinate axes is represented by the ordered pair (x, y).
  • Trigonometry is the science of relationships between the sides and angles of a right-angled triangle.
  • Trigonometric Ratios: Ratios of sides of right triangle are called trigonometric ratios.
    Consider triangle ABC right-angled at B. These ratios are always defined with respect to acute angle ‘A’ or angle ‘C.
  • If one of the trigonometric ratios of an acute angle is known, the remaining trigonometric ratios of an angle can be easily determined.
  • How to identify sides: Identify the angle with respect to which the t-ratios have to be calculated. Sides are always labelled with respect to the ‘θ’ being considered.

However, it is very tedious to write full forms of t-ratios, therefore the abbreviated notations are:
sine A is sin A
cosine A is cos A
tangent A is tan A
cosecant A is cosec A
secant A is sec A
cotangent A is cot A


The topics discussed in this chapter are as follows:

  • Trigonometric Ratios
  • Trigonometric Ratios of Complementary Angles
  • Trigonometric Identities

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(Sin 30°+cos 60°)-(sin 60° + cos 30°) is equal to

sin 30° = ½, sin 60° = √3/2, cos 30° = √3/2 and cos 60° = ½

Putting these values, we get:

(½+½)-(√3/2+√3/2)

= 1 – [(2√3)/2]

= 1 – √3

sin (90° – A) and cos A are

By trigonometry identities.

Sin (90°-A) = cos A {since 90°-A comes in the first quadrant of unit circle}

Hence, both are same.

If cos X = a/b, then sin X is equal to

cos X = a/b

By trigonometry identities, we know that:

sin2X + cos2X = 1

sin2X = 1 – cos2X = 1-(a/b)2

sin X = √(b2-a2)/b

sin 2A = 2 sin A is true when A =

sin 2A = sin 0° = 0

2 sin A = 2 sin 0° = 0

If ∆ABC is right angled at C, then the value of cos(A+B) is

Given that in a right triangle ABC, ∠C = 90°.

We know that the sum of the three angles is equal to 180°.

∠A + ∠B + ∠C = 180° 

∠A + ∠B + 90° = 180° (∵ ∠C = 90° ) 

∠A + ∠B = 90° 

Now, cos(A+B) = cos 90° = 0

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