Trigonometry Study Notes for SSC and Railways Exams

Trigonometry is one of the fundamental concepts in Mathematics. It was first taught by a Greek mathematician named Hipparchus. In Trigonometry, we study and quantify the relation between the sides and the angles of a right-angled triangle.

Trigonometry is also an important topic in most government exams and SSC exams like SSC CGL, CHSL, MTS, Steno, CPO and RRB Exams like RRB NTPC, Group D and others. For an ideal score in the SSC competitive exams, you must prepare Trigonometry well, remember the formulas, and must have sufficient practice of questions.

Trigonometric Functions and Angles 

The functions are studied on a right-angled triangle. The diagonal or the longest length is known as hypotenuse. The other sides are called base and perpendicular.

The angle under consideration lies between base and hypotenuse. The perpendicular is opposite to the angle. Suppose ‘α’ is the angle,

• sin α = perpendicular / hypotenuse
• cos α = base / hypotenuse
• tan α = perpendicular / base
  

Trigonometric Angles

In Trigonometry, angles most commonly used in questions are 0°, 30°, 45°, 60°, and 90°. Here the angle is studied on a right-angled triangle. We can further calculate for 180°, 270°, 360° using the table.

Formulas used in Trigonometry

Given below are some of the most basic and important trigonometric formulas that one must remember while preparing for SSC exams. These formulae are applicable in the case of right-angled triangles only.

• sin2α + cos2α = 1
• tan2α +1 = sec2α
• cot2α +1 = cosec2α
• sin2α = 2sinαcosα
• cos2α = cos2α – sin2α
• tan2α = 2tanα / (1 - tan2α)
• cot2α = (cot2α – 1)/ 2cotα
• sin(α + β) = sin(α)cos(β) + cos(α)sin(β)
• cos(α + β) = cos(α)cos(β) – sin(α)sin(β)
• tan(α + β) = [tan(α) + tan(β)] / [1− tan(α) tan(β)]
• sin(α – β) = sin(α)cos(β) – cos(α)sin(β)
• cos(α – β) = cos(α)cos(β) + sin(α)sin(β)
• tan(α – β) = [tan(α) − tan(β)] / [(1+tan(α) tan(β)]

Tips to Solve Trigonometry Questions

The key to scoring well in the Trigonometry section is:

1. to be well versed in the formulae and relations.
2. to have an adequate practice of questions of all types.
3. to understand and visualize the angles and the sides of the triangle.

Importance of Trigonometry in Competitive SSC & Government Exams

Trigonometry is an important topic as it is featured in most examinations:

• As it is a tough topic and is featured in advanced mathematics sections, it easily confuses examinees.
• Inadequate practice results in incorrect solutions.
• Unprepared Trigonometry results in severe negative marking as it is a major topic.

Most Recommended Books for Trigonometry

The best method to prepare Trigonometry for SSC is to study from relevant books. Some of the most popular books are:

Why prepare Trigonometry from BYJU'S Exam Prep

BYJU'S Exam Prep is an online learning and exam preparation platform. The site caters to almost all entrance exams like the SSC CPO, SSC-CGL, Railways Exam, SSC Stenographer, etc. BYJU'S Exam Prep is an excellent site for preparation as they provide students with:

• Live classes where you can easily interact with the faculty.
• Daily practice tests and quizzes
• Ease of doubt clearing on a discussion board
• Well scheduled preparation strategy
• Teachers who are experts in their respective fields.
• Latest exam notifications

Overall, BYJU'S Exam Prep helps a student from the first step and with their extensive teaching and tests. The student can score well if they study diligently.

A student spends countless hours studying so that they can score a rank in entrance exams. It is therefore important to have a clear and concise approach to preparing a topic. Since Trigonometry is a very important topic, it must be understood and prepared well. 

FAQs

• If (2sin θ - cos θ)/ (cos θ = sin θ) = 1, then the value of cot θ is:

 (a)1/2

 (b)1/3

 (c)3

 (d)2

Answer: (a)1/2

• What is the value of sin (45° + θ) – cos (45° – θ) is

(a)1

(b)0

(c)2cos θ

(d)2sin θ

Answer: (b)0

• Evaluate : ( Cot4 θ – Cosec4θ+ Cot2 θ + Cosec2 θ ) 

(a)1

(b)0

(c)-1

(d) 2

Correct Answer: (b)0

• If 7 sin2 θ + 3 cos2 θ = 4 and 0 ≤ θ ≤ π/2, then the value of tan θ is  :

(a) √3/7

(b)√2/7

(c)1/√3

(d)1/√7

Correct Answer: (c) 1/√3