Trigonometry Most Expected Questions for SSC CGL Tier 2 Exam

Trigonometry for SSC CGL Tier 2 Exam

Trigonometry for SSC CGL Exam: The Staff Selection Commission (SSC) conducts the SSC CGL exam every year. As per the selection process of 2024, the SSC has successfully conducted the SSC CGL Tier 1 exam. As the next step, the SSC will conduct the SSC CGL Tier 2 exam. Passing the Tier 2 exam is not an easy task. For the best preparation for the exam, candidates must prepare topic-wise to get a deep insight into the exam. In this blog, we have provided a basic concept about the trigonometry and most expected questions that can be asked in the SSC CGL Tier 2 exam. Trigonometry is a topic that belongs to the Quantitative Aptitude section in the Tier 2 exam. Candidates can expect at least 5-9 questions from this topic in the SSC CGL Tier 2 exam. Candidates who are going to appear in the exam must go through this blog carefully.

Concept of Trigonometry

Definition:

Trigonometry is a topic of quantitative aptitude that deals with the relationships between the angles and sides of triangles, particularly right-angled triangles. The fundamental concept in trigonometry revolves around the ratios of the sides of a right-angled triangle relative to its angles.

Basic Trigonometric Ratios:

In a right-angled triangle, let:

• θ be one of the non-right angles,
• Opposite be the side opposite to the angle θ,
• Adjacent be the side adjacent to the angle θ,
• Hypotenuse be the side opposite the right angle (the longest side).

The six fundamental trigonometric ratios are defined as:

1. Sine (sin⁡):

2. Cosine (cos⁡):

3. Tangent (tan⁡):

4. Cosecant (csc⁡): (Reciprocal of sine)

5. Secant (sec⁡): (Reciprocal of cosine)

6. Cotangent (cot⁡): (Reciprocal of tangent)

Pythagorean Theorem:

For a right-angled triangle, the relationship between the sides is given by:

Hypotenuse²=Opposite²+Adjacent²

This is a fundamental relationship used to derive many trigonometric identities.

Trigonometric Identities:

1. Pythagorean Identities:

2. Reciprocal Identities:

3. Quotient Identities:

4. Co-function Identities:

Angle Sum and Difference Identities:

1. Sine of sum and difference:

sin(A+B)=sin(A)cos(B)+cos(A)sin(B)
sin⁡(A−B)=sin⁡(A)cos⁡(B)−cos⁡(A)sin⁡(B)

2. Cosine of sum and difference:

cos(A+B)=cos(A)cos(B)−sin(A)sin(B)
cos⁡(A−B)=cos⁡(A)cos⁡(B)+sin⁡(A)sin⁡(B)

3. Tangent of sum and difference:

Double Angle and Half-Angle Formulas:

1. Sine Double Angle:

sin(2θ) = 2 sin(θ) cos(θ)

2. Cosine Double Angle:

cos(2θ) = cos²(θ)−sin²(θ)

or equivalently:

cos(2θ) = 2 cos²(θ) − 1
cos(2θ) = 1−2 sin²(θ)

3. Tangent Double Angle:

4. Half-Angle Formulas:

Law of Sines and Law of Cosines:

These laws are used in any triangle, not just right-angled ones.

1. Law of Sines:

where a,b,c are the sides of the triangle, and A,B,C are the opposite angles.

2. Law of Cosines:

This formula helps find a side of a triangle when two sides and the included angle are known, or it can be used to find angles when all three sides are known.

Trigonometric Functions of Any Angle:

For angles greater than 90°, the values of trigonometric functions can be determined using the unit circle. The unit circle approach defines each of the trigonometric functions for all real angles (not just those in a right triangle).

Most Expected Important Questions PDF for Trigonometry

Question 1: What is the minimum value of 4(sin⁴θ + cos⁴θ – 2sin²θcos²θ)?

A) 1

B) 0

C) -1

D) 4

Question 2: When the altitude of the sun changes from 30° to 45°, the length of the shadow of an electricity pole on level ground decreases by 20 cm. What is the height of the electricity pole?

A) 8(√3 – 1) cm

B) 10(√3 – 1) cm

C) 5(√5 + 1) cm

D) 10(√3 + 1) cm

Question 3: If 3(sin²θ + cos²θ) = 4cos²θ, 0° < θ < 90°, the value of (tan²θ + cos²θ + sec²θ) is:

A) (10/7)

B) (15/19)

C) (29/12)

D) (30/13)

Question 4: The difference between the height of a pole and the length of its shadow is 4(√3 – 1) cm. If the height of the pole is 4√3 cm, then find the angle of elevation of the sun.

A) 60°

B) 45°

C) 30°

D) 90°

Question 5: The value of [sec(70°+ θ) – cosec(20°- θ) – cos²64° – cos²26°]/(sin32°cos58° + cos32°sin58°) is:

A) 0

B) -1

C) 1

D) 2

SSC CGL 2024 Tier 2 Free Preparation Resources

Below we are providing the SSC CGL 2024 Tier 2 Free Preparation Resources that contains multiple tests, including section-wise mock tests covering all the sections like English, General Awareness, Quantitative Aptitude, and Reasoning. Practicing these tests will help you revise all these sections in a time-bound manner and also test your skills and knowledge acquired in the last stretch of revision.

Trigonometry Most Expected Questions for SSC CGL Tier 2 Exam FAQs

• Sign Up on Practicemock for Updated Current Affairs, Free Topic Tests and Free Mini Mocks
• Sign Up Here to Download Free Study Material