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**Trigonometry may appear to be complex**

but is simple if approached the right way. Read on to understand what is

trigonometry along with an explanation of trigonometric ratios.

but is simple if approached the right way. Read on to understand what is

trigonometry along with an explanation of trigonometric ratios.

What is

Trigonometry? Trigonometry is a branch of mathematics that deals with the length

of the side of a triangle and the angles in a triangle. Trigonometry is not a

very common topic in competitive exams, however it is asked in a few exams like

SSC CGL and SSC CHSL where it is given good weightage. Therefore it makes it

essential for us to study this topic. Trigonometric ratios are one of the

fundamental pillars of trigonometry. We will start our series on trigonometry

by discussing the different trigonometric ratios.

Trigonometry? Trigonometry is a branch of mathematics that deals with the length

of the side of a triangle and the angles in a triangle. Trigonometry is not a

very common topic in competitive exams, however it is asked in a few exams like

SSC CGL and SSC CHSL where it is given good weightage. Therefore it makes it

essential for us to study this topic. Trigonometric ratios are one of the

fundamental pillars of trigonometry. We will start our series on trigonometry

by discussing the different trigonometric ratios.

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**What is Trigonometry- Different**

Systems for Measuring an Angle

Systems for Measuring an Angle

There are 3

different ways to measure an angle.

different ways to measure an angle.

*1. Sexagesimal or*

English System: DegreesEnglish System: Degrees

In this system the angle is measured in terms of degrees. As per this system, one right angle constitutes 90°, one degree constitutes

60’ and one minute is 60’’.

60’ and one minute is 60’’.

*2. Centesimal or*

French System: GradesFrench System: Grades

In this system the angle is measure in terms of grade. The

root word of this system is ‘cent’ which means 100, so in this system one right

angle is equal to 100g (g here stands for grades), one grade is

equal to 100’ and each minute is equal to 100’’.

root word of this system is ‘cent’ which means 100, so in this system one right

angle is equal to 100g (g here stands for grades), one grade is

equal to 100’ and each minute is equal to 100’’.

*3. Circular System:*

RadiansRadians

In this system the angle is measure in terms of radians. One

radian (1c) is the angle subtended at the centre of a circle by an

arc of length equal to the radius of the circle.

radian (1c) is the angle subtended at the centre of a circle by an

arc of length equal to the radius of the circle.

On comparing the three systems we can say-

The above relationship can be used to convert an angle in one

system to an angle in the other system.

system to an angle in the other system.

1c = 1 x 180/p = (180 x 7)/22 = 570 17’ 45’’

So remember-

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**What is Trigonometry- Relationship**

between Radius, of the Length Arc and the Angle Subtended at the Centre

between Radius, of the Length Arc and the Angle Subtended at the Centre

Before we move ahead to trigonometric ratios, let us discuss

the relationship between the radius, length of the arc and angle subtended at

the centre, in a circle.

the relationship between the radius, length of the arc and angle subtended at

the centre, in a circle.

Look at the diagram below, where we consider a circle with

radius ‘r’, centre ‘O’ and an arc of length ‘l’.

radius ‘r’, centre ‘O’ and an arc of length ‘l’.

The length of the arc is the product of the

radius and the angle subtended at the centre. (The angle is in terms if

radians)-

radius and the angle subtended at the centre. (The angle is in terms if

radians)-

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**Trigonometric Ratios**

Trigonometric ratios are the simply the ratios of

different sides of a right angled triangle with respect to acute angle. So for

trigonometric ratios we simply take two sides and get their ratios, and based

on the different pair of sides we choose, we get different trigonometric

ratios.

different sides of a right angled triangle with respect to acute angle. So for

trigonometric ratios we simply take two sides and get their ratios, and based

on the different pair of sides we choose, we get different trigonometric

ratios.

Here we have a right angled triangle, which had a 900

angle at the vertex

the initial line is the

the third side is the

θ at the vertex

various trigonometric ratios.

angle at the vertex

**. We know the side opposite to the right angle is called the***A***,***Hypotenuse*the initial line is the

**of the triangle and***Base*the third side is the

**. We also have an angle***perpendicular*θ at the vertex

**. With respect to this angle we are going to consider the***B*various trigonometric ratios.

Stay tuned for more on trigonometry and till then don’t stop practicing!

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