RBSE Class 10 Maths Notes Chapter 8 Introduction to Trigonometry

These comprehensive RBSE Class 10 Maths Notes Chapter 8 Introduction to Trigonometry will give a brief overview of all the concepts.

RBSE Class 10 Maths Chapter 8 Notes Introduction to Trigonometry

Important Points

1. The English word ‘trigonometry’ is derived from the Greek words ‘tri’ (meaning three) ‘gon’ (meaning sides) and ‘metron’ (meaning measure). In fact, trigonometry is the study of relationships between the sides and angles of a triangle.

2. Early astronomers used trigonometry to find out the distances of the stars and planets from the earth. Even today, it is used in Engineering and Physical Sciences.

3. Pythagoras Theorem—“In a right triangle, the sum of the squares of the sides forming a right angle is equal to the square of the hypotenuse.” (AC)² – (AB)² + (BC)²
With the help of this theorem, if the measures of two sides are known to us, then we can find the measure of third side.

4. Trigonometric Ratio—The study of some ratios of the sides of a right triangle with respect to its acute angles is called trigonometric ratio.

According to the figure

5. Trigonometric Ratio of Reciprocals –

(1) \(\frac{1}{\sin \theta}\) = Cosec θ ⇒ sin θ Cosec θ = 1
(2) \(\frac{1}{\cos \theta}\) = sin θ ⇒ Cos θ sec θ = 1
(3) \(\frac{1}{\tan \theta}\) = Cot θ ⇒ tan θ Cot θ = 1

Cosec A = \(\frac{1}{\sin A}\) ,sec A = \(\frac{1}{\cos \mathrm{A}}\)
tan A = \(\frac{1}{\cot \mathrm{A}}\),tan A = \(\frac{\sin A}{\cos A}\)

6. If one of the trigonometric ratio of an acute angle is known, then the remaining trigonometric ratios of that angle can be determined easily.

7. The value of sin A or cos A never exceeds 1, whereas the value of sec A or cosec A is always greater than or equal to 1.

8. Table of trigonometric ratios of specific angles

9. Trigonometric Ratios of Complementary Angles—Complementary Angles—

Two angles are said to be complementary if their sum equal 90°.
sin (90° – θ) =  cos θ cot (90°- θ)  = tan θ
cos (90° – θ) = sin θ  see (90°- θ) = cosec θ
tan (90°- θ) = cot θ  cosec (90° – θ) = sec θ

Thus sine of any angle = cosine of its complementary angle tangent of any angle = cotangent of its complementary angle secant of any angle = cosecant of its complementary angle Their converse is also true.

10. Trigonometric Identities—The identity related with trigonometric ratios of an angle is called a trigonometric identity. While proving the trigonometric identities, the following points must be remembered.

• We start with solution in complex side of the identity and using the fundamental identities in it we find the other side.
• If a number of trigonometric ratio are present in the identities, then it remain generally convenient to express them in the form of sine or cosine.
• If radical sign is involved then that must be removed as far as possible.
• If from one side of identity, the other side cannot be found easily, then simplifying both the sides, we should prove each of them identically equal to only one quantify’ or term.

11. Square Relation
(1) sin² θ + cos² θ =1
⇒ sin² θ = 1- cos² θ or cos² θ=1- sin² θ

(2) sec² θ – tan² θ= 1
⇒ sec² θ =1+ tan² θ or tan² θ = sec² θ – 1

(3) cosec² θ – cot² θ = 1
⇒ cosec² θ=1+ cot² θ or cot² θ = cosec² θ – 1