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Trigonometry for SSC CGL: Formula, Tricks, Questions
By BYJU'S Exam Prep
Updated on: September 25th, 2023
SSC CGL Trigonometry is a significant component of the exam syllabus. Due to its intricate formulas and challenging questions, Trigonometry is a significant aspect of the Quantitative Aptitude section. Trigonometry is the branch of maths that deals with the angles and lengths of a right-angled triangle. It is one of the most critical topics in the quantitative aptitude section as at least 2 to 3 trigonometry questions are based on this topic.
In this article, we will provide you all with the Trigonometry Questions for SSC CGL, important SSC CGL Trigonometry formulas, and questions asked in SSC CGL exams over the years. Bookmark this page if you want complete information regarding the Trigonometry section for SSC CGL.
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SSC CGL Trigonometry
Trigonometry is one of the most significant branches of mathematics, with numerous applications in a wide range of fields. The study of the relationship between the sides and angles of a right-angle triangle is the focus of the Trigonometry branch. As a result, using trigonometric formulas, functions, or trigonometric identities, it is possible to find the missing or unknown angles or sides of a right triangle. Angles in trigonometry can be measured in degrees or radians. 0°, 30°, 45°, 60°, and 90° are some of the most widely utilized trigonometric angles for calculations.
In this blog, we are going to provide complete Trigonometry notes for SSC CGL including formulas and questions. Let’s begin!
Trigonometry Formulas for SSC CGL
There are 6 main Trigonometric functions namely, Sin, Cos, Tan, Sec, Cosec, and Cot. All Trigonometric functions, formulas and tricks are derived from these 6 functions. Below is the list of important Trigonometry formulas for SSC CGL 2023 and other competitive exams.
Let’s start with the values of different angles in different quadrants:
(1) In the hexadecimal system, the angles are measured in degrees, minutes and seconds.
One complete rotation = 360 degrees (360^{0}) 1^{0} = 60 minutes (60’); 1’ = 60 seconds (60”)
In the circular system, the angles are measured in radians. π radians (π^{c}) = 180^{0}
^{}
(2) Let S = length of arc AB
θ = angle AOB expressed in radians and r = radius of the circle
Then, S = r × θ
(3) And the area of sector AOB is A = (1/2) × r^{2} × θ
(4) Consider the right angle triangle ABC as shown
Sine θ = Opposite Side/Hypotenuse = BC/AC
Cosine θ = Adjacent Side/Hypotenuse = AB/AC
Tangent θ = Opposite Side/Adjacent Side = BC /AB
Cosec θ = 1/sinθ
Sec θ = 1/cos θ
Cot θ = 1/tan θ
(5) Limiting Value of the Trigonometrical Ratios
- Since sin² θ + cos² θ = 1, hence each of sin θ and cos θ is numerically less than 1; or their maximum value is 1.
- Since sec θ and cosec θ are respectively reciprocals of cos θ and sin θ, therefore the values of sec θ and cosec θ are always greater than 1; or their minimum value is 1.
- tan θ and cot θ can have any value between – infinity and + infinity.
(6) Signs Of Trigonometrical Ratios
1. Quadrant: 0 to 90, All + ve
2. Quadrant: 90° to 180°, only sin θ and cosec θ + ve, rest – ve
3. Quadrant: 180° to 270°, only tan θ and cot θ + ve, rest – ve
4. Quadrant: 270° to 360°, only cos θ and sec θ + ve, rest – ve
(7) Trigonometrical Ratios Of Allied Angles
1. sin ( – θ) = – sin θ; cosec (- θ) = – cosec θ
cos ( – θ) = cos θ; sec (- θ) = sec θ;
tan ( – θ) = – tan θ; cot (- θ) = – cot θ
2. Trigonometric ratios of (90° – θ) in terms of those of θ, for all values of θ:
sin (90° – θ) = cos θ; cosec (90° – θ) = sec θ
cos (90° – θ) = sin θ; cosec (90° – θ) = cosec θ
tan(90° – θ) = cot θ; cot (90° – θ) = tan θ
3. sin (90° + θ) = cos θ; cosec (90° + θ) = sec θ
cos (90° + θ) = – sin θ; cosec (90° + θ) = – cosec θ
tan(90° + θ) = – cot θ; cot (90° + θ) = tan θ
4. sin (180° – θ) = cos θ; cosec (180° – θ) = cosec θ
cos (180° – θ) = – cos θ; cosec (180° – θ) = sec θ
tan(180° – θ) = – tan θ; cot (90° -θ) = – cot θ
Important Points:
- Since angles 360° – θ and (- θ) are coterminal angles, the trigonometric ratios of (360° – θ) and (- θ) must be identical.
- Since angles 360° – θ and θ are coterminal angles, the trigonometric ratios of 360° + θ and θ must be identical.
Maximum and Minimum Value Trigonometric Identity:
Type-I:
In case of sec^{2}x, cosec^{2}x, cot^{2}x and tan^{2}x, we cannot find the maximum value because they can have infinity as their maximum value. So in question containing these trigonometric identities, you will be asked to find the minimum values only. The typical question forms are listed below:
Example: -1
Find the Minimum value of 9 cos ^{2}x + 2 sec ^{2}x
sol – this equation is a typical example of our type-3 so apply the formula 2√ ab so,
- Minimum Value = 2√ 9 x 2= 2√ 18
Example:-2
Find the Minimum value of 8 tan ^{2}x + 7 cot ^{2}x
sol – this equation is a typical example of our type-3 so apply the formula 2√ ab so,
- Minimum Value = 2√ 8 x 7= 2√ 56
Type -II:
Example -1
Find the Maximum and Minimum Value of 3 sin x + 4 cos y
Sol- If you find the question of this kind, apply the above formulae.
- Maximum Value = √ 9 + 16 = √ 25 = 5
- Minimum Value = – √ 9 + 16 = – √ 25 = – 5
Example-2
Find the Maximum and Minimum Value of 3 sin x + 2 cos y
Sol- If you find the question of this kind, apply the above formulae.
- Maximum Value = √ 9 + 4 = √ 13
- Minimum Value = – √ 9 + 4 = – √ 13
Type III:
Example -1
Find the maximum and Minimum Value of 3 sin ^{2}x + 4 cos ^{2}x
Sol- Here the 4> 3 so
- Maximum Value = 4
- Minimum Value = 3
Example –2
Find the maximum and Minimum Value of 5 sin ^{2}x + 3 cos ^{2}x
Sol – Here 5>3
- Maximum Value = 5
- Minimum Value = 3
Type-IV
Find the Minimum Value of Sec ^{2}x + cosec ^{2}x
Sol – 1 + tan ^{2}x + cosec ^{2}x ——————————————–(Sec ^{2}x = 1 + tan ^{2}x)
= 1+ tan ^{2}x + 1 + cot ^{2}x ————————————————(cosec ^{2}x = 1 + cot ^{2}x )
=2 + tan ^{2}x + cot ^{2}x—————————————————apply type-3 formula
=2 + 2 √ 1 x 1 = 2 + 2 =4
SSC CGL Trigonometry Questions
Below we are going to provide you all with the important SSC CGL Trigonometry questions. These are the types of questions that are asked in the CGL and other Government examinations.
1. Evaluate : ( Cot^{4 }Θ – Cosec^{4 }Θ + Cot^{2 }Θ + Cosec^{2 }Θ )
A. 1
B. 0
C. -1
D. 2
Correct Answer: B
2. If 7 sin^{2} Θ + 3 cos^{2 }Θ = 4 and 0 ≤ Θ ≤ π/2, then the value of tan Θ is :
A. √3/7
B. √2/7
C. 1/√3
D. 1/√7
Correct Answer: C
3. If x = a cos^{3} Θ, y = b sin^{3} Θ, then
(x/a)^{2/3 }+(y/b)^{2/3} = ?
A. 1
B. 0
C. 2
D. 4
Correct Answer: A
4. The value of cot 2π/20 x cot 4π/20 x cot 5π/20 x cot 6π/20 x cot 8π/20 is
B. 0
C. 1
D. 3
B. 3
C. 2/3
D. 1
6.△ABC is a right-angle triangle and a right-angle at B. If cotA = 15/8, then sin A + sin B + sin C will be equal to:
A. 17/40
B. 25/8
C. 40/17
D. 8/25
Answer ||| C
7.If sinx – 2cosx = √2cosx, then find the value of cotx is _______.
A. 2 – √2
B. 2 – √2
C. √2
D. (2 – √2)/2
Answer ||| D
8.What is the value of the expression 100(sin 15° cos 15°)?
A. 50
B. 75
C. 100
D. 25
Answer ||| D
9.Find the value of the following.
A.
B.
C.
D. √3
Answer ||| D
10.The value of sin18^{0} is given as . Using this value, find the value of cos72^{0}.
B.
C.
D.
Answer ||| A
11.If tanθ + cotθ = 6, then find the value of tan^{2}θ + cot^{2}θ + 2
A. 10
B. 12
C. 16
D. 36
Answer ||| D
12. If cos x + cos y = 2, the value of sin x + sin y is
A. 0
B. 1
C. 2
D. -1
Correct Answer: A
B. 2
C. 3
D. 1
Correct Answer: B
B. 0
C. -1
D. 2
B. 1/√3
C. √3/2
D. 1
B. 12
C. 10
D. 8
SSC Trigonometry Questions with Solutions PDF
If you look at the recent 4-5 years of SSC CGL or other competitive exam papers, you will notice that many questions from Trigonometry are asked. Because the questions are based on previous year’s papers, candidates may encounter numerous questions from the Trigonometry questions PDF. Therefore, keeping in mind the need of aspirants we are providing SSC Trigonometry questions with solutions PDF below:
SSC Trigonometry Questions with Solutions PDF (Click Here)
Best Book for Trigonometry for SSC CGL
To score well and earn a job in the government sector, aspirants must thoroughly prepare for the exam. While there are many tools accessible for exam preparation, books are regarded as one of the most important. You can undoubtedly get useful information regarding the best book for Trigonometry in this article. So put an end to your worries and consider consulting these SSC CGL books, which can simply help you obtain a deeper comprehension of this topic for the upcoming exam.
- Lucent’s Higher Mathematics Part 2 – Rishikesh Kumar
- Kiran’s SSC Mathematics – Algebra, Trigonometry, geometry, and mensuration – Think tank of Kiran publications
- NCERT Maths by NCERT – Grade 6 to 12
- Online Quiz (thousands of questions to practice are available) by BYJU’S Exam Prep
Trigonometry Weightage in SSC CGL
This segment is time-consuming and takes a lot of practice. It is recommended that you concentrate more on this portion and carefully answer all of the questions. Trigonometry weightage in SSC CGL depends on various shifts and the difficulty level of the examination. Check out the data provided below regarding the weightage of the Trigonometry section in SSC CGL :
Tier |
No. of Questions |
Difficulty Level |
Tier 1 |
3-4 |
Easy-Moderate |
Tier 2 |
4-5 |
Moderate |
Tips to Prepare for Trigonometry for SSC CGL
The Staff Selection Commission Combined Graduate Level (SSC CGL) exam is extremely competitive, and many applicants find Trigonometry from the Quantitative Aptitude component difficult. Here are some preparation suggestions and tactics for the Trigonometry section in the SSC CGL exam:
- To be fully informed of the formulae and linkages.
- Must have an adequate practice of questions of all varieties.
- To grasp and visualise the angles and the sides of the triangle.
- Try to solve questions using the options.
- Don’t mug up the formulas.
We have learned about Trigonometry in the simplest manner possible with detailed information. To get more information on this section along with step-by-step solutions to all questions subscribe to our SSC Online Classroom Program and download the app to get personalized content and SSC mock test series.