## 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 h2 =b2+p2.

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) sin2Î¸+cos2⁡Î¸=1

(iv) sec2Î¸-tan2Î¸=1

(v) cosec2Î¸-cot2⁡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¸