Introduction of Trigonometry

The word ‘trigonometry’ is derived from the Greek words ‘trigon’ and ‘metron’ and it means ‘measuring the sides of a triangle’.

Angles, Vertex, Initial Side, Terminal Side

Angle is a measure of rotation of a given ray about its initial point. The original ray is called the initial side and the final position of the ray after rotation is called the terminal side of the angle. The point of rotation is called the vertex.

Degree measure

If a rotation from the initial side to terminal side is (1/360)^th of a revolution, the angle is said to have a measure of one degree, written as 1°.
A degree is divided into 60 minutes, and a minute is divided into 60 seconds. One sixtieth of a degree is called a minute, written as 1′, and one sixtieth of a minute is called a second, written as 1″. Thus, 1° = 60′, 1′ = 60″.
e.g., 360°, 180° etc.

Radian measure

There is another unit for measurement of an angle, called the radian measure. Angle subtended at the centre by an arc of length 1 unit in a unit circle (circle of radius 1 unit) is said to have a measure of 1 radian.
e.g., 1, -1 etc.

Relation between Degree and Radian

A circle subtends at the centre an angle whose radian measure is 2π and its degree measure is 360°, it follows that 2π radian = 360° or π radian = 180°
The above relation enables us to express a radian measure in terms of degree measure and a degree measure in terms of radian measure. Using approximate value of π as 22/7.
1 Radian = 180°/π = 57° 16′ approximately.
1 Degree = π/180 Radian = 0.01746 Radian approximately.
The relation between degree measures and radian measure of some common angles are given in the following table:

Notational Convention

Radian Measure = 180°/π x Degree Measure
Degree Measure = π/180 x Radian Measure

Some Trigonometric Functions of Table

Note :-

All Trigonometric Functions are placed in formulae.

Sign of Trigonometric Functions

The signs of other trigonometric functions in different quadrants. In fact, we have the following table.

Domain and range of Trigonometric Functions

The Domain and range of Trigonometric Functions some common angles are given in the following table:

Trigonometric Identities.

The sum and difference of two numbers (angles) and related expressions. The basic results in this connection are called trigonometric identities.

Note :-

All Trigonometric Identities are placed in formulae.

Trigonometric Equations

Equations involving trigonometric functions of a variable are called trigonometric equations.

Principal solutions

The solutions of a trigonometric equation for which 0 ≤ x < 2π are called principal solutions.

General solution

The expression involving integer ‘n’ which gives all solutions of a trigonometric equation is called the general solution.