Trigonometry Tricks for Competitive Exams (SSC)

Trigonometry is an another important chapter from competition point of view basically SSC. Since in last few years SSC asked many questions from this chapter but very few questions asked in IBPS. First of all I would like to clear you the base concept of this chapter.

Trigonometry :- Trigonometry is a branch of Mathematics which deals in triangles and the relationship between their sides and angles and these relationships can be made using the trigonometric functions and ratios.

Angle:- When two straight non-parallel lines in a plain intersect each other, the inclination formed between them is known as angle between those two lines.       

Figure of angle

Triangle :- Triangle is a figure bounded by three non- parallel straight lines intersecting each other, having three vertices, angles with the condition that “Sum of all interior angles is equal to 180⁰.

         i.e.                         angle A +angle B + angle C = 180⁰

Triangles are classified under two sections :-

·         Classification based on sides.

·         Classification based on angles.

Classification Based on Sides :- Triangles are of three types under this category of classification :-

1.      Scalene Triangle (Triangle with all sides of different length.)

2.      Isosceles Triangles (Triangle with any two sides of same length)

3.      Equilateral Triangles (Triangle with all sides of same length and angles of same measure 60⁰)

Classification Based on Angles :- Triangles are of three types under this category of classification :-

1.      Acute- angled Triangle (Triangle with all angles of different measure less than 90⁰)

2.      Right- angled Triangle (Triangle with any one angle of measure 90⁰.)

3.      Obtuse-angled Triangle (Triangle with any one angle of measure more than 90⁰)

Right- Angled Triangle :-Right-angled triangle is a figure bounded by three non- parallel straight lines intersecting each other such that any two lines intersecting perpendicularly (means angle formed between them is 90⁰) and having three vertices, angles with the condition that “Sum of all interior angles is equal to 180⁰.

In the above figure

                                   Side AB is known as Perpendicular denoted as “P”

                                   Side BC is known as Hypotenuse denoted as “H”

                                   Side BC is known as Base denoted as “B”

Trigonometric Ratios: The ratio between two sides of right-angled triangle are known as trigonometric ratios. 

The base ratios are

                                                       Sinθ = P/H

                                                      Cosθ = B/H

                                                      Tanθ = Sinθ/Cosθ = (P/H) × (H/B) = P/B

The above three ratios have one brother each which are related inversely with them. Let’s see this relationship :-

                                  Cosecθ = 1/Sinθ = H/P

                                  Secθ = 1/Cosθ = H/B

                                  Cotθ = 1/Tanθ = Cosθ/ Sinθ = (B/H) × (H/P) = B/P.

  Hence we can say that

                    Sinθ and Cosecθ are brothers which are related to each-other inversely.

                      Cosθ and Secθ are brothers which are related to each-other inversely.

                    Tanθ and Cotθ are brothers which are related to each-other inversely.

This implies that   :-

Sinθ × Cosecθ = 1 Cosθ × Secθ = 1 Tanθ × Cotθ = 1

           

  

  Hope you have enjoyed the base concept of this chapter till now. More Conceptual enjoyment will be continued for you soon, just keep visiting this blog regularly and writing me your related queries through comment or forum.

Best of Luck for Exams. To be continued soon........................

Sinθ × Cosecθ = 1

Cosθ × Secθ = 1

Tanθ × Cotθ = 1