## Revision Notes for Ch 8 Introduction to Trigonometry Class 10th Mathematics

**Trigonometry and Trigonometric Ratios**

→ Trigonometry is the branch of mathematics which deals with measurements of angles and the problems related to relationship between sides and angles.

**Trigonometric Ratios:**

→ It is the ratios of two sides of a right angle triangle.

→ Suppose we have a right angled triangle ABC.

→ Thus the trigonometric Ratios are defined as the largest side of a right angle triangle is known as hypotenuse.

Also, by Pythagoras theorem, we know that h

^{2}=b

^{2}+p

^{2}.

Here, Î¸ is pronounced as theta, ∠A=Î¸. We write trigonometric ratios according to angle Î¸.

**Trigonometric Ratios for Few Particular Angels**

**Note:-**Some Angles like cosecÎ¸ for Î¸=0° is not defined. We know that cosecÎ¸ = 1/sinÎ¸ = 1/0. 1/0 is not defined hence cosec0° is not defined.

**Trigonometric Identities**

→ Identities are equations which are valid for any conditions. Trigonometric identities are equations involving trigonometric ratios.

**Some Trigonometric Identities are:**

(i) sin

^{2}Î¸+cos

^{2}Î¸=1

(iv) sec

^{2}Î¸-tan

^{2}Î¸=1

(v) cosec

^{2}Î¸-cot

^{2}Î¸=1

**Trigonometric Ratios for Complementary Angles**

(i) sin (90 – Î¸) = cosÎ¸

(ii) cos (90 – Î¸) = sinÎ¸

(iii) tan (90 – Î¸) = cotÎ¸

(iv) cot (90 – Î¸) = tanÎ¸

(v) sec (90 – Î¸) = cosecÎ¸

(vi) cosec (90 – Î¸) = secÎ¸