Topic Quantitative Abilities for SSC-CGL 2020

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:

1.  sin2Ө+ cos2 Ө=1
2. tan2 Ө+1= sec2 Ө
3. cot2 Ө+1= cosec2 
4. sin(-Ө)= -sin Ө
5. cos(-Ө)= cos Ө
6. tan(-Ө)= -tan Ө
7. cosec(-Ө)= - cosec Ө
8. sec(-Ө)=sec Ө
9. cot(-Ө)=-cot Ө
10. tan Ө=sin Ө/cos Ө
11. sec Ө= 1/cos Ө
12. 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 

1. 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,

1. Sin (900- Ө) = Cos Ө 
2. Tan (900- Ө) = Cot Ө
3. Cot (900- Ө) = Tan Ө
4. Sec (900- Ө) = Cosec Ө
5. Cosec (900- Ө) = Cosec Ө