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Trigonometry CAT Questions: The CAT exam 2024 includes three sections: VARC, DILR & QA. Students need to prepare for each CAT section diligently and be informed about updated CAT exam patterns as well. The trigonometry is a part of the CAT quant section. The questions of trigonometry fall under Geometry. To know more about trigonometry and its types of questions, continue reading the blog post below.
Table of Contents
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
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Trigonometry CAT Questions PDF: Download Here
Download the Trigonometry CAT questions PDF given below:
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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.
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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.
| Degrees | 0° | 30° | 45° | 60° | 90° | 180° | 270° | 360° |
| Radians | 0 | π/6 | π/4 | π/3 | π/2 | π | 3π/2 | 2π |
| 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 |
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Basic Trignometric Ratios
The basic trigonometric ratios are mentioned below:
- sin of ∠A = sin A = Side opposite to ∠A/ Hypotenuse
- cosin of ∠A = cos A = Side adjacent to ∠A/ Hypotenuse
- cotangent of ∠A = cot A = 1/tan A = (Side adjacent to ∠A)/ (Side opposite to ∠A)
- tan of ∠A = tan A = (Side opposite to ∠A)/ (Side adjacent to ∠A)
- cosecant of ∠A = cosec A = 1/sin A = Hypotenuse/ Side opposite to ∠A
- secant of ∠A = sec A = 1/cos A = Hypotenuse/ Side adjacent to ∠A
- Also, tan A = sin A/cos A
- 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 |
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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°.
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FAQs
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.
Therefore, as per the basic Trigonometry formula, Sin A = BC/AC. cos A = AB/AC. tan A = BC/AB.
Within the quantitative aptitude section, a significant component is trigonometry.
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