**Introduction**

**Trigonometry is an important branch of mathematics.**

** Trigonometry is a Greek word. The word Trigonometry has been divided into three phases.**

## 1 **TRI** mean **THREE**

## 2 **GONI** mean** ANGLES**

## 3 **MERTON** mean **MEASUREMENT**

**it is clear that Trigonometry means** **MEASUREMENT**.

**Unit of Measures of angles.**

**What is angle.**

**Two rays have the same initial points make an angle with each other.**

**The starting point is called the initial point and the other is called the ending point or terminating point.**

**PROPERTY OF Triangle**

The **hypotenuse **is always the **longest side** and it is the **opposite of the right-angle**.

The **opposite **side of the triangle that side is ** opposite **to the

**angle**.

The **adjacent **side is the side that is * adjacent to *the

**angle**.

you can check the **Rotation of axes** for further concepts.

## COMPLEX Number

A **complex number** is a **number** that can be expressed in the form x+yi,

where x and y are real **numbers**, and i is a symbol called the imaginary part of complex no.

And satisfying the equation i^{2} = −1. Because no “real” **number** satisfies this equation,

In some way, it is the only “number” that we can square and get a negative value.

definition all the square roots in the following.

√−16=4i√−100=10i√−5=√5i√−28=√28i

## CIRCLE

The distance from the center we called the radius.

And the point is called the center. Two times the radius is known as the diameter.

## GROUP

**Group theory**,

The study of groups, which are systems consisting of a set of elements and binary operations.

That can be applied to two elements of the set which together satisfy.

These require that the be closed under the operation that it obeys the associative law

That it contains an identity element zero or 1

. If the group also satisfies the commutative law it is called a commutative, or abelian, group.

in the group, the identity element is 0

and all the properties satisfied are called the group and if commutative property satisfied is called an abelian group.

**MATRICES**

A matrix is a rectangular array of numbers symbols and expressions that are arranged in

rows and columns. **element**: is called matrices.

SOME IMPORTANT MATRICES

**row vector**: A matrix with a single row

**column vector**: A matrix with a single column

**square matrix**: A matrix that has an equal number of rows and columns is called a square matrix.

**matrix**: A rectangular array of numbers, symbols, expressions, arranged in rows and columns

**VECTOR**

definition of a vector. **Vectors that have the same magnitude as well as direction. **

This means that if we take a vector and translate it to a new position

a vector we obtain at the end of this process is the same vector we had in the beginning.

- Vectors are added geometrically.
- Vectors whose resultant have to be calculated behave independently of each other.
- Vector Addition is by using head to tail rule nothing but finding the resultant of a number of vectors acting on a body.
- Vector Addition is commutative. This means that the resultant vector is independent of the order of vectors.