Trigonometry CAT Questions: Concepts, Formulas to Prepare | Download Sample CAT Trigonometry Questions PDF

By Aditi Joshi|Updated : November 19th, 2022

CAT Trigonometry Questions are a part of the Geometry section and are asked under the QA section of CAT. However, it has been seen that the Trigonometry CAT Questions are rarely asked in the exam. As the CAT Authorities do not prescribe the syllabus, it cannot be assumed that CAT Trigonometry Questions are not included in the syllabus.

It has been seen that Trigonometry Questions for CAT have been asked once in 5-6 years. The candidates should practice CAT Trigonometry Questions, although the frequency of the questions asked is negligible. In this article, BYJU'S Exam Prep experts have given all the details related to Trigonometry Questions for CAT to assist the candidates in their preparation.

Table of Content

What are CAT Trigonometry Questions?

Trigonometry CAT Questions involve formulae-based questions. The candidates should learn basic concepts for CAT Trigonometry Questions in order to ace the CAT Exam. To begin with, it is important to understand the basic concepts of hypotenuse, base, and perpendicular.

CAT Trigonometry Questions

In a Right Triangle such as ABC

  • AC is the Hypotenuse of the triangle.
  • AB is the perpendicular of the triangle.
  • BC is the base of the triangle.

Therefore, as per the basic Trigonometry formula,

  • Sin A = BC/AC
  • cos A = AB/AC
  • tan A = BC/AB
  • cosec A = 1/ sin A
  • sec A = 1/ cos A
  • cot AA = 1/ tan A

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Table of Angles for CAT Trigonometry Questions

The table of angles for Trigonometry CAT Questions helps to find the values of standard angles. The table consists of trigonometric ratios such as sine, cosine, tangent, cosecant, secant, cotangent. Candidates with complete knowledge of the table of angles can solve CAT Trigonometry Questions easily. Given below is the table of angles:

Degrees

30°

45°

60°

90°

180°

270°

360°

Radians

0

π/6

π/4

π/3

π/2

π

3π/2

Sin θ

0

1/2

1/√2

√3/2

1

0

-1

0

Cos θ

1

√3/2

1/√2

1/2

0

-1

0

1

Tan θ

0

1/√3

1

√3

0

0

Cot θ

√3

1

1/√3

0

0

Sec θ

1

2/√3

√2

2

-1

1

Cosec θ

2

√2

2/√3

1

-1

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Definitions and Fundamental identities of CAT Trigonometry

Note the table below to get an idea of the fundamental identities which you need to know to solve CAT Trigonometry Questions.

Parameter

Details

Reciprocal Identities

sin θ = 1/(cos θ)

csc θ = 1/(sin θ)

cos θ = 1/(sec θ)

sec θ = 1/(cos θ)

tan θ = 1/(cot θ)

cot θ = 1/(tan θ)

Quotient Identities

tan θ = (sin θ)/(cos θ)

cot θ = (cos θ)/(sin θ)

Pythagorean Identities

sin²θ + cos²θ = 1

tan2θ + 1 = sec2θ

cot2θ + 1 = cosec2θ

sin 2θ = 2 sin θ cos θ

cos 2θ = cos²θ – sin²θ

tan 2θ = 2 tan θ / (1 – tan²θ)

cot 2θ = (cot²θ – 1) / 2 cot θ

Negative Angle Identities

sin(−θ) = − sin θ

cos(−θ) = cos θ

tan(−θ) = − tan θ

sec(−θ) = sec θ

cot(−θ) = − cot θ

CAT Trigonometry Questions: Complementary Angle Theorem

  • If two acute angles add up to be 90°, they are considered complementary
  • The following are considered cofunctions:
    • sine and cosine
    • tangent and cotangent
    • secant and cosecant
  • The complementary angle theorem says that cofunctions of complementary angles are equal.

☛ See Also: How to Get 99 Percentile in CAT

Trigonometry CAT Questions PDF

Candidates need to solve the different types of CAT Trigonometry CAT Questions available. Candidates aspiring to take the CAT can check the BYJU'S Exam Prep App for CAT Trigonometry Questions for practice. Click on the link below to download a PDF file of Trigonometry Questions for CAT.

Download CAT Trigonometry Questions PDF

Trigonometry Questions for CAT: Sample

In order to ace the CAT Trigonometry CAT Questions, the candidates must practice questions based on trigonometry regularly. As there is no fixed CAT Syllabus, the candidates should not ignore this topic. Given below are some of the sample Trigonometry CAT Questions for reference:

Question 1: The maximum value of 3 cosx + 4 sinx + 8 is —------?

Answer: 13

Explanation:

 

CAT Trigonometry Questions

Question 2: The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower.

Answer: 10√3 m

Explanation:

Here, b = 30 m, Angle of Elevation = 30º

tan 30º = p/30

⇒ 1/√3 = p/30

⇒ p = 10√3

∴ Height = 10√3 m

Question 3: If cos4θ - sin4θ = 3/4, then the value of 2cos2θ – 1 is:

Answer: 0.75

Explanation:

Given: cos4θ - sin4θ = ¾

We know that x2 − y2 = (x − y)(x + y)

So, (cos2θ − sin2θ)(cos2θ + sin2θ) = ¾

⇒ (cos2θ − sin2θ) = ¾

⇒ (cos2θ − 1 + cos2θ) = ¾

⇒ 2cos2θ − 1 = 3/4

Question 4: If sin(x + y) = cos(x – y), then the value of cos2x is:

Answer: ½

Explanation:

Given:

sin(x + y) = cos(x – y)

⇒ sin(x + y) = sin(90° – x + y)

⇒ x + y = 90° – x + y

⇒ 2x = 90°

⇒ x = 45°

Therefore, cos2x = cos245° = = 1/2

How to Prepare CAT Trigonometry Questions?

In order to solve Trigonometry CAT Questions, the candidates need to have a strong grip on trigonometry formulae. Additionally, always try to represent the given questions diagrammatically to understand the flow and tricks of the questions. The candidates should solve CAT Previous Year Question Paper and mock tests to understand the type and difficulty level of CAT Trigonometry Questions.

Best Books for Trigonometry CAT Questions

Candidates can solve CAT Trigonometry Questions from different Quantitative Ability books available in the market. It is always suggested that the candidates should choose the CAT Books of renowned authors/publishers. Candidates can check the BYJU'S Exam Prep App for study notes based on CAT Trigonometry Questions and also attempt the practice questions. They can also get a detailed understanding of the topic by watching the live sessions on BYJU'S Exam Prep App.

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FAQs on CAT Trigonometry Questions

  • CAT Trigonometry Questions are rarely asked in the exam. To ensure that you are fully prepared for the CAT, practice the Trignometry questions PDF mentioned here along with the CAT Question papers. As CAT does not prescribe any syllabus, the candidates should practice Trigonometry CAT Questions.

  • Candidates need to practice the previous year's question papers and mock tests in order to crack CAT Trigonometry Questions. Candidates can solve the BYJU’S Exam Prep Mock tests to understand the type of questions asked in the exam. 

  • Trigonometry CAT Questions are rarely asked however, the candidates should practice questions on trigonometry as the CAT exam has no defined syllabus. On the basis of past trends, it has been observed that the frequency of Trigonometrical CAT Questions is less. 

  • There are no maximum and minimum Trignometry CAT Questions. However, it has been seen that Trignometry Questions have not been asked in the recent CAT exam. But it is important to remember that Trigonometry Questions in CAT can be solved easily if the candidates have good knowledge about Trigonometric Ratios. Candidates should solve the previous year's question papers so that they have an understanding of the type of questions asked in the exam.

  • Yes, the candidates can prepare for CAT Trigonometry Questions by self-study. They only need to study the formulas well and revise those concepts simultaneously by practising the previous year's questions.

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