class 11

CONTENTS OF THIS PAGE:

What is Trigonometry?

Trigonometric ratios

Trigonometric identities

Sums based on identities of Trigonometry

Matrices

Types of Matrices

What is a 2 x 2 matrix

What is a 3 x 3 matrix

Determinants

Sums based on properties of determinants

Adjoint of a matrix

Cramer's Rule

Distance Formula

Section Formula

Three Dimensional Geometry Octants

TRIGONOMETRY:

It is a branch of Mathematics that deals with angles and sides of a triangle.

The six ratios of trigonometry are as follows:

Sine (sin)

Cosine (cos)

Tangent (tan)

Cotangent (cot)

Cosecant (cosec)

Secant (sec)

BASIC IDENTITIES OF TRIGONOMETRY:

sin2θ + cos2θ = 1

1 + tan2θ = sec2θ

1 + cot2θ = cosec2θ

A trigonometric equation is an equation involving one or more trigonometric ratios. Trigonometric sums are proved using both algebraic identities and trigonometric identities as shown in the examples below:

TRIGONOMETRY

SUMS USING TRIGONOMETRIC IDENTITIES

MATRIX:

it is an arrangement of elements in rows and columns. The horizontal line is called the row and the vertical line is the column. The order of a matrix of m rows and n columns is given by m x n.

DETERMINANT:

It is the value obtained by multiplying the elements of the matrix using a particular method row wise or column wise.

Types of matrices:

A row matrix has only one row with any number of columns.

A column matrix has only one column with any number of rows.

A square matrix has equal number of rows and columns.

An identity matrix is a matrix that has the main diagonal elements as 1 and all other elements as zero.

A singular matrix is a matrix with determinant value equal to zero.

A non singular matrix is a matrix whose determinant is a non zero value.