Trigonometry Study Resources for Competitive Exams

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Trigonometry MCQ & Objective Questions

Trigonometry is a crucial branch of mathematics that plays a significant role in various school and competitive exams. Mastering this topic not only enhances your understanding of angles and their relationships but also boosts your confidence in tackling objective questions. Practicing MCQs and important questions in Trigonometry helps solidify concepts and improves your exam preparation, ensuring you score better in your assessments.

What You Will Practise Here

Fundamental Trigonometric Ratios: Sine, Cosine, and Tangent
Trigonometric Identities and Their Applications
Graphs of Trigonometric Functions
Inverse Trigonometric Functions
Applications of Trigonometry in Real-Life Problems
Solving Right-Angled Triangles
Height and Distance Problems

Exam Relevance

Trigonometry is a vital topic in various examinations, including CBSE, State Boards, NEET, and JEE. Questions often focus on fundamental concepts, problem-solving, and application-based scenarios. Common patterns include direct MCQs, numerical problems, and theoretical questions that assess your understanding of trigonometric principles and their applications.

Common Mistakes Students Make

Confusing the ratios of different angles, especially in right-angled triangles.
Misapplying trigonometric identities in problem-solving.
Neglecting to check the domain and range of inverse trigonometric functions.
Overlooking the importance of unit circle in understanding trigonometric functions.

FAQs

Question: What are the basic trigonometric ratios?
Answer: The basic trigonometric ratios are Sine, Cosine, and Tangent, which relate the angles of a triangle to the lengths of its sides.

Question: How can I improve my Trigonometry skills for exams?
Answer: Regular practice of Trigonometry MCQ questions and understanding the underlying concepts will significantly enhance your skills and exam readiness.

Now is the time to take charge of your Trigonometry preparation! Dive into our practice MCQs and important questions to test your understanding and excel in your exams.

Heights & Distances Trigonometric Ratios & Identities

Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the point is 10 meters away from the base of the hill, what is the height of the hill?

A. 10 meters
B. 5 meters
C. 15 meters
D. 20 meters

Solution

Let h be the height of the hill. tan(45°) = h/10. Therefore, h = 10 * tan(45°) = 10 * 1 = 10 meters.

Correct Answer: A — 10 meters

Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the distance from the point to the base of the hill is 10 meters, what is the height of the hill?

A. 10 meters
B. 5 meters
C. 15 meters
D. 20 meters

Solution

Using tan(45) = height/10, height = 10 * tan(45) = 10 meters.

Correct Answer: A — 10 meters

Q. From a point on the ground, the angle of elevation to the top of a hill is 53.13 degrees. If the point is 40 meters away from the base of the hill, what is the height of the hill?

A. 30 meters
B. 40 meters
C. 50 meters
D. 20 meters

Solution

Using the tangent function, tan(53.13) = height / 40. Therefore, height = 40 * tan(53.13) = 40 * 1.6 = 64 meters.

Correct Answer: A — 30 meters

Q. From a point on the ground, the angle of elevation to the top of a tower is 30 degrees. If the tower is 20 meters tall, how far is the point from the base of the tower?

A. 20√3 meters
B. 10√3 meters
C. 30 meters
D. 40 meters

Solution

Using the tangent function, tan(30) = 20 / distance. Therefore, distance = 20 / tan(30) = 20√3 meters.

Correct Answer: A — 20√3 meters

Q. If a tree casts a shadow of 10 meters and the angle of elevation to the top of the tree is 30°, what is the height of the tree?

A. 5√3
B. 10
C. 10√3
D. 5

Solution

Height = shadow * tan(30°) = 10 * (1/√3) = 10/√3 = 5√3.

Correct Answer: A — 5√3

Q. If cos(θ) = 0.5, what is θ in degrees?

A. 30°
B. 60°
C. 90°
D. 45°

Solution

cos(30°) = 0.5, so θ = 30°.

Correct Answer: A — 30°

Q. If cos(θ) = 0.6, what is sin²(θ)?

A. 0.36
B. 0.64
C. 0.8
D. 0.2

Solution

Using the identity sin²(θ) + cos²(θ) = 1, sin²(θ) = 1 - 0.6² = 0.64.

Correct Answer: B — 0.64

Q. If the angle of elevation from a point 30 meters away from the base of a hill is 60 degrees, what is the height of the hill?

A. 15√3 meters
B. 30 meters
C. 20 meters
D. 10√3 meters

Solution

Using the tangent function, tan(60) = height / 30. Therefore, height = 30 * tan(60) = 30 * √3 = 30√3 meters.

Correct Answer: A — 15√3 meters

Q. If the angle of elevation from a point 50 meters away from a tower is 60 degrees, what is the height of the tower?

A. 25√3 meters
B. 50 meters
C. 43.3 meters
D. 30 meters

Solution

Using the tangent function, tan(60) = height / 50. Therefore, height = 50 * tan(60) = 50 * √3 ≈ 86.6 meters.

Correct Answer: A — 25√3 meters

Q. If the angle of elevation from a point 50 meters away from the base of a hill is 30 degrees, what is the height of the hill?

A. 25 meters
B. 50 meters
C. 15 meters
D. 20 meters

Solution

Using tan(30) = height/50, height = 50 * (1/√3) = 50/√3 = 25 meters.

Correct Answer: A — 25 meters

Q. If the angle of elevation from a point 50 meters away from the base of a tower is 30 degrees, what is the height of the tower?

A. 25 meters
B. 50 meters
C. 10√3 meters
D. 15 meters

Solution

Let h be the height of the tower. tan(30°) = h/50. Therefore, h = 50 * tan(30°) = 50 * (1/√3) = 50/√3 = 25√3/3 meters.

Correct Answer: A — 25 meters

Q. What is the height of a building if it casts a shadow of 20 meters when the angle of elevation is 45°?

A. 10
B. 20
C. 20√2
D. 40

Solution

Height = shadow * tan(45°) = 20 * 1 = 20.

Correct Answer: B — 20

Q. What is the height of a building if the angle of elevation from a point 50 meters away is 45°?

A. 50
B. 25
C. 100
D. 75

Solution

Using tan(45°) = height/50, height = 50 * tan(45°) = 50.

Correct Answer: A — 50

Q. What is the inverse of sin(1/2)?

A. 30°
B. 45°
C. 60°
D. 90°

Solution

The inverse of sin(1/2) is 30°.

Correct Answer: A — 30°

Q. Which of the following is equivalent to sin(θ + 90°)?

A. cos(θ)
B. sin(θ)
C. tan(θ)
D. sec(θ)

Solution

sin(θ + 90°) = cos(θ) by the co-function identity.

Correct Answer: A — cos(θ)

Q. Which of the following is the correct formula for the sine of a sum?

A. sin(a + b) = sin(a) + sin(b)
B. sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
C. sin(a + b) = sin(a)sin(b)
D. sin(a + b) = cos(a) + cos(b)

Solution

The sine of a sum is given by sin(a + b) = sin(a)cos(b) + cos(a)sin(b).

Correct Answer: B — sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

Q. Which of the following is the definition of cotangent?

A. 1/tanθ
B. cosθ/sinθ
C. sinθ/cosθ
D. tanθ/cosθ

Solution

cot(θ) = 1/tan(θ).

Correct Answer: A — 1/tanθ

Q. Which of the following is true for all angles θ?

A. sin(θ) = cos(90° - θ)
B. tan(θ) = sin(θ) + cos(θ)
C. sec(θ) = 1/tan(θ)
D. csc(θ) = sin(θ)

Solution

sin(θ) = cos(90° - θ) is a co-function identity.

Correct Answer: A — sin(θ) = cos(90° - θ)

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