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.
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.
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 | 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 |
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.
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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:
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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