#### Topics

##### Number Systems

##### Real Numbers

##### Algebra

##### Pair of Linear Equations in Two Variables

- Linear Equation in Two Variables
- Graphical Method of Solution of a Pair of Linear Equations
- Substitution Method
- Elimination Method
- Cross - Multiplication Method
- Equations Reducible to a Pair of Linear Equations in Two Variables
- Consistency of Pair of Linear Equations
- Inconsistency of Pair of Linear Equations
- Algebraic Conditions for Number of Solutions
- Simple Situational Problems
- Pair of Linear Equations in Two Variables
- Relation Between Co-efficient

##### Arithmetic Progressions

##### Quadratic Equations

- Quadratic Equations
- Solutions of Quadratic Equations by Factorization
- Solutions of Quadratic Equations by Completing the Square
- Nature of Roots of a Quadratic Equation
- Relationship Between Discriminant and Nature of Roots
- Situational Problems Based on Quadratic Equations Related to Day to Day Activities to Be Incorporated
- Application of Quadratic Equation

##### Polynomials

##### Geometry

##### Circles

- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
- Tangent to a Circle
- Number of Tangents from a Point on a Circle
- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles

##### Triangles

- Similar Figures
- Similarity of Triangles
- Basic Proportionality Theorem (Thales Theorem)
- Criteria for Similarity of Triangles
- Areas of Similar Triangles
- Right-angled Triangles and Pythagoras Property
- Similarity of Triangles
- Application of Pythagoras Theorem in Acute Angle and Obtuse Angle
- Triangles Examples and Solutions
- Angle Bisector
- Similarity of Triangles
- Ratio of Sides of Triangle

##### Constructions

##### Trigonometry

##### Heights and Distances

##### Trigonometric Identities

##### Introduction to Trigonometry

##### Statistics and Probability

##### Probability

##### Statistics

##### Coordinate Geometry

##### Lines (In Two-dimensions)

##### Mensuration

##### Areas Related to Circles

##### Surface Areas and Volumes

- Concept of Surface Area, Volume, and Capacity
- Surface Area of a Combination of Solids
- Volume of a Combination of Solids
- Conversion of Solid from One Shape to Another
- Frustum of a Cone
- Concept of Surface Area, Volume, and Capacity
- Surface Area and Volume of Different Combination of Solid Figures
- Surface Area and Volume of Three Dimensional Figures

##### Internal Assessment

## Definition

Trignometric ratios are ratios of two sides of a right triangle and a related angle.

## Notes

A]Trignometric ratios of an acute angle of a right triangle-

Let take ∠A as θ

AC is a hypotenuse. Hypotenuse is the longest side in a right angled triangle and it is opposite of the right angle.

Now, here θ will decide the base and perpendicular in a right angled triangle.

The side on which θ lies is known as base, and the side opposite to θ is known as perpendicular. In the above figure AB is the base and BC is the perpendicular.

There exist six trignometric ratios, sin, cos, tan, cot, sec and cosec, and they are as follows,

1)sinθ= `"Perpendicular"/"hypotenuse" = "BC"/"AC"`

2)cosθ= `"base"/ "hypotenuse"= "AB"/"AC"`

3)tanθ= `"perpendicular"/"base"= "BC"/"AB"`

4)cotθ= `"base"/ "perpendicular"= "AB"/"BC"`

5)secθ= `"hypotenuse"/ "base"= "AC"/"AB"`

6)cosecθ= `"hypotenuse"/ "perpendicular"= "AC"/"BC"`

Similarly, if we take,

Here, Let take ∠C as θ

AC is the hypotenuse, BC is the base and AB is the perpendicular.

The ratios will be,

1)sinθ= `"AB"/"AC"`

2)cosθ= `"BC"/"AC"`

3)tanθ= `"AB"/"BC"`

4)cotθ= `"BC"/"AB"`

5)secθ= `"AC"/"BC"`

6)cosecθ= `"AC"/"AB"`

B] Reciprocal Relation-

1) cosecθ= `1/sin theta`

2) secθ= `1/ cos theta`

3) cotθ= `1/tan theta`

4) sinθ= `1/(cosec theta)`

5) cosθ= `1/sec theta`

6) tanθ= `1/cot theta`

C] Power of Trigonometric ratios-

1) `(sin theta)^2`= `sin^2 theta`

2) `sin^2 theta`= `(sin theta)^2`

3) `(cos theta)^3`= `cos^3 theta`