** Quantitative Abilities**

The **SSC** has **online** notified **SSC** **CGL new vacancy 2020 **for the aspirants preparing for competitive exams.

The candidates must go through the **SSC** website **online **to get the** **detailed requirements and syllabus for the exam.

**Degree and Radian Measures**

These two measures are used to measure the angles in the field of mathematics.

Degree:

- This is a mathematical unit to measure the size of the angle with its direction.
- Degree can be represented in the form of 3600 circles.
- When a unit degree is divided by 60, it is converted into unit minute.

10= 60 minute

Or 1 minute= 10/60

**Radian**:

- This is also a measurement unit of angle which measures the size of the angle.
- An angle subtended by an arc equal to the radius of the circle makes 1 radian or 1 rad angle to the center.

If the angle on the center is Ө then

Ө= Length of Arc/ radius of the circle

For **example**, if the arc length of a circle is 10meter and radius of the circle is 5 meter, then the value of Ө will be

Ө= 10/5=2 radian or 2 rad

Conversion from degree to radian:

Radian= 1800/π

Degree= π/1800

Conversion of 1radian or 1 rad into degree the following process can be used.

n radian= n* 1800/π

For **example**, n=1

1 radian= 1*1800/π

= 1800/3.14 (Take value of π=22/7 or 3.14)

**1 radian = 57.320**

**Note:** These calculations are used to solve problems on the clock.

**SSC CGL 2020: Standard Identities**

A standard identity is the one in which the left side of the equation gives the same result as the right-hand side of the equation when variables in the equation are replaced with a constant value.

For **example**,

Take value of Ө=300

Take the identity sin2Ө + cos2 Ө=1

Put Ө=300 in the equation

sin2300 + cos2 300=1

(1/2)2+ (√3/2)2=1

1/4+3/4=1

4/4=1

**1=1**

Some of the standard identities of trigonometry are as follows:

- sin2Ө+ cos2 Ө=1
- tan2 Ө+1= sec2 Ө
- cot2 Ө+1= cosec2
- sin(-Ө)= -sin Ө
- cos(-Ө)= cos Ө
- tan(-Ө)= -tan Ө
- cosec(-Ө)= - cosec Ө
- sec(-Ө)=sec Ө
- cot(-Ө)=-cot Ө
- tan Ө=sin Ө/cos Ө
- sec Ө= 1/cos Ө
- cosec Ө=1/sin Ө

**SSC CGL 2020: Complementary Angles**

In trigonometry, two angles are said to be complementary if the sum of the two angles is 900.

x and (900-x) are two complementary angles.

For **example**, we put x=300 than complementary angle of 300 will be (900- 300) = 600

In trigonometry

- Sin Ө= Cos (900- Ө)

For **example**, Take Ө=300, take left-hand side of the formula:

sin300=1/2

Right-hand side of the formula:

Cos (900- Ө) = Cos (900- 300)

= Cos 600

=1/2

So the value of both the side of formula is equal.

Likewise,

- Sin (900- Ө) = Cos Ө
- Tan (900- Ө) = Cot Ө
- Cot (900- Ө) = Tan Ө
- Sec (900- Ө) = Cosec Ө
- Cosec (900- Ө) = Cosec Ө