Trigonometry CAT Questions: Sample Questions, Formulas, and Definitions

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Trigonometry CAT Questions

Trigonometry CAT Questions: CAT exam 2024 includes three sections: VARC, DILR & QA. Students need to prepare for each CAT section more diligently and be informed about updated CAT exam patterns as well. The trigonometry is a part of CAT quant section. The questions of trigonometry fall under the geometry. To know more about trigonometry and its types of questions, continue reading the blog post below. 

Trigonometry CAT Questions (Sample Questions)

Here are a few sample questions related to trigonometry as per CAT examination. 

Q1. If cos A + cos2 A = 1 and a sin12 A + b sin10 A + c sin8 A + d sin6 A – 1 = 0. Find the value of a+b/c+d

A) 4

B) 3

C) 6

D) 1

Answer: 3

Q2. Find the maximum and minimum value of 8 cos A + 15 sin A + 15

A) 11√2+15

B) 30; 8

C) 32; -2

D) 23; 8

Answer: 32; -2

Q3. 3sinx + 4cosx + r is always greater than or equal to 0. What is the smallest value ‘r’ can to take?

A) 5

B) -5

C) 2

D) 3

Answer: -5

In the below figure, the sheet of width W is folded along PQ such that R overlaps S Length of PQ can be written as :-

A) w/sin2αcosα

B) w/cosα(1+sin2α)

C)  24

D) Any two of the above

Answer: Any two of the above

Trigonometry CAT Questions PDF: Download Here

Download the Trigonometry CAT questions PDF here:

Trigonometry Sample Questions CAT.pdf

What is Trigonometry?

The word trigonometry is derived from the Greek word tri meaning three, gon meaning sides and metron meaning measure. It is a study related to the sides and angles of a triangle. The three basic trigonometry functions are sine, cosine and tangent. Other essential equations are derived from cotangent, secant and cosecant. 

Table of Angles for CAT Trigonometry Questions

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

Degrees30°45°60°90°180°270°360°
Radians0π/6π/4π/3π/2π3π/2
Sin θ01/21/√2√3/210-10
Cos θ1√3/21/√21/20-101
Tan θ01/√31√300
Cot θ√311/√300
Sec θ12/√3√22-11
Cosec θ2√22/√31-1

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.

ParameterDetails
Reciprocal Identitiessin 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 Identitiestan θ = (sin θ)/(cos θ)
cot θ = (cos θ)/(sin θ)
Pythagorean Identitiessin²θ + 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 Identitiessin(−θ) = − sin θ
cos(−θ) = cos θ
tan(−θ) = − tan θ
sec(−θ) = sec θ
cot(−θ) = − cot θ
Source: Unacademy CAT

Basic Trignometric Ratios

The basic trigonometric ratios are mentioned below: 

  1. sin of ∠A = sin A = Side opposite to ∠A/ Hypotenuse
  2. cosin of ∠A = cos A = Side adjacent to ∠A/ Hypotenuse
  3. cotangent of ∠A = cot A = 1/tan A = (Side adjacent to ∠A)/ (Side opposite to ∠A)
  4. tan of ∠A = tan A = (Side opposite to ∠A)/ (Side adjacent to ∠A)
  5. cosecant of ∠A = cosec A = 1/sin A = Hypotenuse/ Side opposite to ∠A
  6. secant of ∠A = sec A = 1/cos A = Hypotenuse/ Side adjacent to ∠A
  7. Also, tan A = sin A/cos A
  8. cot A = cos A/sin A
Trigonometric Ratios of Complementary Angles
sin (90° – A) = cos A
cos (90° – A) = sin A
tan (90° – A) = cot A
cot (90° – A) = tan A
sec (90° – A) = cosec A
cosec (90° – A) = sec A
Trignometric Identities
cos2A + sin2A = 1
1 + tan2A = sec2A
cot2A + 1 = cosec2A

Special Triangle Ratio

Two triangles that have the same trigonometric ratio value regardless of the length of their sides. Two triangles have the same trigonometric ratio value regardless of the length of their sides. These two triangles have sides with angles 45°-45°-90° and 30°-60°-90°.

Related Reads

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Best DILR Book for CAT 2024 PreparationCAT Previous Year Exam Papers: Download PDF for Practice
VARC Topics for CAT: Important Topics, Syllabus, Tips to PrepareImportant Topics in DILR for CAT with Preparation Tips
DILR Syllabus for CAT 2024: Important Topics, WeightageImportant Topics in DILR for CAT with Preparation Tips

FAQs

How many questions come from trigonometry in CAT?

It appears in questions about geometry. In the CAT exam, questions in geometry are worth 20% of the total. Though there won’t be any straight questions on trigonometry in the CAT Question Paper, knowing the fundamentals will help you answer the 20% weighted geometry questions.

What is the formula for trigonometry in CAT?

Therefore, as per the basic Trigonometry formula, Sin A = BC/AC. cos A = AB/AC. tan A = BC/AB.

Is trigonometry part of a CAT exam?

Within the quantitative aptitude section, a significant component is trigonometry.

This was all Trigonometry CAT Questions. For more informative blogs, check out our Management Exams Section, or you can learn more about us by visiting our  Indian exams page of Leverage Edu.

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