COMEDK UGET 2025 Trigonometry Practice Questions with Solutions

COMEDK UGET 2025 Trigonometry Practice Questions with Solutions: Trigonometry is one of the most important chapters in the COMEDK UGET exam syllabus. If you are preparing for COMEDK entrance exam, you should pay special attention to Trigonometry to score good marks in the Mathematics paper. The chapter covers various sub-topics, like Measurement of Angles, Trigonometric Functions etc. from the 11th and 12th Class syllabus. While the majority of the topics are well known, you should solve as many COMEDK Trigonometry practice questions as you can to improve accuracy while preparing for the exam. Trigonometry for COMEDK UGET 2025 exam covers an approximate weightage of around 10-13% and you can expect 6-8 questions from this chapter. In this article, we have provided some of the most important COMEDK UGET 2025 Trigonometry practice questions with solutions to help you assess your knowledge and preparation for the upcoming test.

Also Check - Do or Die Chapters for COMEDK UGET 2025 Mathematics

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COMEDK UGET 2025 Trigonometry Important Topics

Before starting with COMEDK Trigonometry practice questions, you should check the important topics mentioned in COMEDK UGET 2025 Mathematics syllabus . The Trigonometry chapter features various fundamental topics such as Positive and Negative angles, Trigonometric functions, Trigonometric identities, and signs of Trigonometric functions. In the following table, we have provided the complete list of topics in Trigonometry chapter for COMEDK UGET 2025:

COMEDK UGET 2025 Trigonometry Expected Weightage

Trigonometry in COMEDK UGET 2025 question paper features around 10-13% weightage with 6-8 questions. You should also check COMEDK UGET previous year question papers to identify which subtopic carries the highest and lowest weightages. You can check the detailed COMEDK UGET 2025 Trigonometry expected weightage here:

COMEDK UGET 2025 Trigonometry Practice Questions with Solutions

Once you are done covering the entire syllabus, test your knowledge and preparation level by solving COMEDK Trigonometry sample questions. These questions are almost accurate or similar to the questions asked in the examination. Our experts have compiled some of the most expected Trigonometry practice questions based on the past couple of years' paper trends. You can check the most important COMEDK UGET 2025 Trigonometry practice questions with solutions below:

Q1. If Sin A = 4/5 and Cos B = -12/13. Where A and B lie in the first and third quadrant respectively. Then Cos (A+B) =?

a. -16/65

b. 16/65

c. 65/16

d. -65/16

Ans. a. -16/65

Solution: We know that,

Cos (A+B) = CosA.CosB - SinA.SinB

First, we need to find the values of CosA and SinB

Since A lies in the first quadrant, both CosA and SinB are positive. We can use the Pythagorean identity to find CosA

Cos ² A + Sin ² A = 1

Substituting Sin A = 4/5

Cos ² A + (4/5) ² = 1

Cos ² A = 9/25 = CosA = 3/5

Since B lies in the third quadrant, both CosB and SinB are negative. We can again use the Pythagorean identity to find Sin B.

Cos ² B + Sin ² B = 1

Substituting Cos B = -12/13

(-12/13) ² + Sin ² B = 1

Sin ² B = 1-(144/169)

Sin ² B = 25/169 = SinB =  - 5/13 (Negative sign because B is in third quadrant)

Now substituting all the values in Cos (A+B) = CosA.CosB - SinA.SinB

(3/5) (-12/13) – (4/5)(-5/13)

= -36/65 + 20/65 = -16/65

Q2. If Sin 2x = 4 cosx, then x is equal to

a. nⲡ/2 ± ⲡ/4, n ∊ Z

b. 2nⲡ ± ⲡ/2, n ∊ Z

c. nⲡ ± ⲡ/2, n ∊ Z

d. None of the above

Ans. b. 2nⲡ ± ⲡ/2, n ∊ Z

Solution: We have Sin 2x = 4 Cos x

2 SinxCosx  = 4Cosx

Cos(Sin x -2) = 0

Cos x = 0 (Sin x ≠ 2)

Cos x = 0 = Cos ⲡ/2 = x = 2nⲡ ± ⲡ/2, n ∊ Z.

Q3. The function f(x) = tan ^-1 (Sin x + Cos x) is an increasing function in?

a. (ⲡ/4, ⲡ/2)

b. (0, ⲡ/2)

c. (-ⲡ/2, ⲡ/4)

d. (-ⲡ/2, ⲡ/2)

Ans. c. (-ⲡ/2, ⲡ/4)

Solution: To determine where the function f(x) = tan ^-1 (Sin x + Cos x) is increasing, we need to analyze its derivative. A function is increasing where its derivative is positive.

First, let's find the derivative of f(x). Given f(x) = tan ^-1 (sin x + cos x), from chain rule:

Let, u = sin x + cos x. Then, f(x) = tan ^-1 (u) and

d/dx[tan ^-1 (u)] = 1/(1+u ² )du/dx

Next, we calculate du/dx

u = sin x + cos x

So, du/dx = cos x - sin x

Thus, f’(x) = 1/[1+(sin x + cos x) ² ].(Cos x – Sin x)

To find where f’(x) > 0, examine the equation,

Cos x – Sin x > 0

Rewriting this, we have

Cos x > Sin x

To identify the intervals where Cos x > Sin x. let's take a look at the behavior of the basic trigonometric functions. We know that:

Cos x = Sin x, where x = ⲡ/4 + kⲡ for any integer k,

In the interval (-ⲡ/2, ⲡ/4), Cos x is generally greater than Sin x.

Verifying the intervals provided, we conclude that Cos x > Sin x holds true for x ∊ (-ⲡ/2, ⲡ/4),

Hence, the function, f(x) = tan-1(Sin x + Cos x) is an increasing function in (-ⲡ/2, ⲡ/4).

Q4. A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having a fence are of the same length x The maximum area enclosed by the park is:

a. √(x3/8

b. ⲡx2

c. 3/2x2

d. 1/2x2

Ans. d. 1/2x2

Solution: To determine the maximum area enclosed by the triangular park, we need to consider that the park is bound by two sides of equal length, x, and the third side by the river. One optimal configuration for maximum area in such cases is an isosceles triangle where the third side (formed by the river) is also a variable.

Let's denote the length of the third side by river as y. The angle between the two sides of length x will be Ө. The area of a triangle formed by two sides and the included angle is given by:

A = 1/2ab SinӨ

Where, a = x, b = x, are the sides of the park. Substituting values, we get,

A = 1/2 x ² SinӨ

To find the angle that maximizes SinӨ, and thus A, we note that SinӨ reaches the maximum value of 1, when Ө = 90°. This description provides for a right angle triangle. In this specific optimally configured triangle:

The base is x,

The height is x,

The angle between x and x is 90°. Thus the maximum area of the triangle will be,

Amax = 1/2x ² Sin90° = 1/2x ² (1) = 1/2x2.

Q5. If Sin 3Ө = Sin Ө, how many solutions exist such that, -2ⲡ < Ө < 2ⲡ

a. 9

b. 8

c. 7

d. 6

Ans. a. 9

Solution: Sin 3Ө = Sin Ө,

3Sin Ө – 4Sin3Ө = Sin Ө

4Sin3Ө – 2SinӨ = 0

2SinӨ (2Sin2Ө – 1) = 0

SinӨ = 0 or Sin Ө = ± 1/√2

If SinӨ = 0, and if SinӨ = ± 1/√2

Ө = 0, ⲡ, – ⲡ

Ө = ⲡ/4, 3ⲡ/4, –5ⲡ/4, –7ⲡ/4, –ⲡ/4, –3ⲡ/4, 5ⲡ/4, 7ⲡ/4

There are 9 solutions.

In addition to solving COMEDK important questions on Trigonometry, make it a habit to attempt mock tests regularly, at least twice or thrice a week. COMEDK UGET 2025 mock test will help you not only with practice and revision but also improve your time management skills and confidence level.

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