Trigonometry Questions for RRB NTPC, Download Free PDF

Hey, Railway aspirant! When you look at the Numerical Ability section for the RRB NTPC exam, you might think of Arithmetic first, but here’s a secret: Trigonometry is one of the quickest, most scoring topics to master. Trigonometry questions are very straightforward. You can expect at least 2 to 3 direct, simple, formula-based questions that check your understanding of basic trigonometric ratios and standard angle values. These questions are purely based on formulas and known values. If you know formulas like tan θ or values such as sin 30°, you can solve them instantly. In this blog, we’ve provided exam-level Trigonometry questions for the RRB NTPC exam in a free downloadable PDF. But before you download it, take a few free Trigonometry tests to analyze your understanding of this topic.

Concept of Trigonometry for RRB NTPC

Trigonometry is the study of the relationship between the sides and angles of a right-angled triangle.

The whole concept revolves around six basic ratios, known as trigonometric functions:

Key Formulas You Must Master

Success in this topic depends entirely on instantly recalling and applying the correct definitions and standard values. Memorize these essentials for the RRB NTPC exam:

Basic Ratios (SOH CAH TOA)
sin θ = Opposite / Hypotenuse
cos θ = Adjacent / Hypotenuse
tan θ = Opposite / Adjacent

Pythagorean Identities
sin²θ + cos²θ = 1
sec²θ – tan²θ = 1
csc²θ – cot²θ = 1

Complementary Angles
sin(90° – θ) = cos θ
tan(90° – θ) = cot θ
sec(90° – θ) = csc θ

Key Scoring Patterns You Must Master (Standard Values)

For the NTPC exam, questions often test your knowledge of specific angles. This table is your goldmine—memorize it!

Angle (θ)	sin θ	cos θ	tan θ
0°	0	1	0
30°	1/2	√3/2	1/√3
45°	1/√2	1/√2	1
60°	√3/2	1/2	√3
90°	1	0	Undefined

Trigonometry Questions for RRB NTPC PDF, Download for Free

The questions asked in the RRB Numerical Ability section are typically direct-substitution problems. They require quick recall of the formula or the value and accurate calculation. They are the perfect type of question that can save you time for other time-consuming sections. To help you master these quick facts, we have provided a PDF containing the most important and frequently asked Trigonometry exam questions. Click the button below to download the free Trigonometry Questions for RRB NTPC PDF.

Q1. If A, B, and C are angles of a triangle, then sin^2 A + sin^2 B + sin^2 C – 2 cos A cos B cos C =?
a) 0
b) 1
c) 2
d) 4

Answer: c

Q2. What is the value of sin(B-C) * cos(A-D) + sin(A-B) * cos(C-D) + sin(C-A) * cos(B-D) = ?
a) 3/2
b) -3
c) 1
d) 0

Answer: d

Q3. If (mx / cos θ) + (ny / sin θ) = m^2 – n^2, and mx * sin^3 θ – ny * cos^3 θ = 0,

then (mx)^(2/3) + (ny)^(2/3) = ?
a) (m^2 – n^2)^(2/3)
b) (m^2 + n^2)^(2/3)
c) (m^2 * n^2)^(2/3)
d) (m^2 – n^2)^(3/2)

Answer: a

Q4. If a * cos^3 θ + 3a * sin^2 θ * cos θ = m, and a * sin^3 θ + 3a * sin θ * cos^2 θ = n,

then (m+n)^(2/3) + (m-n)^(2/3) = ?
a) a^(2/3)
b) 2 * a^(2/3)
c) (a * sin θ * cos θ)^(2/3)
d) 2 * a^(1/3)

Answer: b

Q5. If tan^2 α = 1 + 2 * tan^2 β, then

√2 * cos α – cos β = ?
a) 0
b) 1
c) 2
d) √2

Answer: a

Q6. If 2y * cos θ = x * sin θ, and 2x * sec θ – y * cosec θ = 3,

then x^2 + 4y^2 = ?
a) 1
b) 2
c) 0
d) 4

Answer: d

Q7. If tan θ – cot θ = a, and cos θ + sin θ = b,

then (b^2 – 1) * (a^2 + 4) = ?
a) 2
b) 1
c) 0
d) 4

Answer: d

Q8. If cot θ + tan θ = x, and sec θ – cos θ = y,

then (x^2 * y)^(2/3) – (x * y^2)^(2/3) = ?
a) 4
b) 3
c) 2
d) 1

Answer: d

Q9. If sin θ + sin 2θ = x, and cos θ + cos 2θ = y,

then (x^2 + y^2) * (x^2 + y^2 – 3) = ?
a) 2y
b) 3y
c) 4y
d) 5y

Answer: a

Q10. If cosec θ – sin θ = x, and sec θ – cos θ = y,

then x^(2/3) * y^(2/3) * (x^(2/3) + y^(2/3)) = ?
a) 0
b) 1
c) -1
d) 2

Answer: b

Preparation Tips for RRB NTPC Trigonometry Questions

Trigonometry is an easy score-maker if you follow a dedicated strategy. These tips will help you maximize your problem-solving skills for this topic:

1. Master the Tables (Mandatory): Start by memorizing the standard trigonometric values for 30°, 45°, and 60°, along with the core Pythagorean identities. These form the backbone of fast and accurate trigonometric calculations.

2. Learn SOH-CAH-TOA: Always keep the basic ratio definitions in mind—

• Sin = Opposite / Hypotenuse
• Cos = Adjacent / Hypotenuse
• Tan = Opposite / Adjacent
  These should be your first reference in any side-based trig problem.

3. Practice Triples: Commit the common Pythagorean triplets (3–4–5, 5–12–13, 8–15–17) to memory. They allow you to determine missing sides quickly whenever only sin or tan is involved.

4. Practice High Volume: Trigonometry is a speed-and-accuracy topic. Build both by solving 10–15 focused questions daily—use free topic-wise tests to maintain consistent repetition.

5. Know the Complementary & Co-function Angles:
Remember that certain trigonometric ratios turn into each other when angles add up to 90°. This helps you solve problems instantly without extra calculations.

• sin θ = cos (90° − θ)
• tan θ = cot (90° − θ)
• sec θ = cosec (90° − θ)

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