Chapter 8

Introduction to Trigonometry

Definition: Trigonometry is the branch of mathematics that deals with triangles and circles. Trigonometry is defined as the study of right triangles; "Tri" is the Ancient Greek word for three, "gon" means side, "metry" measurement: together they make "measuring three sides".

Value of:

= 180° (in degree) and 3.14 or 22/7 (Approx. in decimal)

Pythagoras Theorem: Pythagoras is used on a right angled triangle. According to this theorem, “The Square of the hypotenuse is equal to the sum of the squares of other two sides”.

(Hypotenuse)² = (Altitude)²+ (Base)²

Trigonometric Ratio: Trigonometric ratios are the relationship between angles and sides of a right angled triangle.

Trigonometric Ratios of Some Specific Angles:

Method to find the ‘sine’ of some specific angles (0°, 30°, 45°, 60° & 90°):

Table of Trigonometric Ratios of Some Specific Angles:

Remark: From the table, you can observe that as increases from 0° to 90°, sin A increases from 0 to 1 and cos A decreases from 1 to 0.

Trigonometric Ratios of Complementary Angles:

Two angles are complementary, if the sum of angles is 90°.

In a right angled triangle, measure of one angle is 90° and sum of other two angles is also 90°. So, these angles are complementary angles.

For any angle A, trigonometric ratios of complementary angle are:

Trigonometric Identities: An equation involving trigonometric ratios of an angle is called a trigonometric identity, if it is true for all values of the angle(s) involved.

For any angle,