Graphs of Trigonometric Functions for Competitive Exams

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Graphs of Trigonometric Functions

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Graphs of Trigonometric Functions MCQ & Objective Questions

The study of Graphs of Trigonometric Functions is crucial for students preparing for school and competitive exams in India. Understanding these graphs not only enhances conceptual clarity but also boosts your confidence in tackling MCQs and objective questions. Regular practice with these important questions can significantly improve your exam performance and help you score better.

What You Will Practise Here

Understanding the basic shapes of sine, cosine, and tangent functions.
Identifying key features such as amplitude, period, and phase shift.
Analyzing transformations of trigonometric graphs.
Exploring the relationships between different trigonometric functions through their graphs.
Solving problems related to the intersections of trigonometric graphs with axes.
Interpreting real-world scenarios using trigonometric graphs.
Practising important Graphs of Trigonometric Functions MCQ questions with detailed solutions.

Exam Relevance

Graphs of Trigonometric Functions are a significant part of the syllabus for CBSE, State Boards, NEET, and JEE. Questions related to this topic often appear in various formats, including direct graph interpretation, transformations, and applications in real-life problems. Familiarity with common question patterns will help you tackle these effectively during your exams.

Common Mistakes Students Make

Confusing the amplitude and period of trigonometric functions.
Overlooking the effects of phase shifts on the graph's position.
Misinterpreting the intersections of graphs with the x-axis and y-axis.
Neglecting to consider the domain and range of trigonometric functions.
Failing to apply transformations correctly when shifting or stretching graphs.

FAQs

Question: What are the key features of the sine and cosine graphs?
Answer: The sine graph has an amplitude of 1, a period of 2π, and oscillates between -1 and 1. The cosine graph shares similar features but starts at its maximum value of 1.

Question: How can I effectively prepare for questions on trigonometric graphs?
Answer: Regularly practice MCQs, focus on understanding the transformations, and review common mistakes to enhance your grasp of the topic.

Now is the time to strengthen your understanding of Graphs of Trigonometric Functions! Dive into our practice MCQs and test your knowledge to excel in your exams.

Q. At what value of x does the function y = tan(x) have a vertical asymptote?

A. 0
B. π/4
C. π/2
D. π

Solution

The tangent function has vertical asymptotes at x = π/2 + nπ, where n is an integer. The first asymptote in [0, π] is at π/2.

Correct Answer: C — π/2

Q. For the function y = sin(3x), what is the period?

A. π
B. 2π
C. 3π
D. 6π

Solution

The period is calculated as 2π divided by the coefficient of x, which is 3, giving a period of 2π/3.

Correct Answer: A — π

Q. What is the amplitude of the function y = 3cos(2x)?

A. 1
B. 2
C. 3
D. 4

Solution

The amplitude is the coefficient in front of the cosine function, which is 3.

Correct Answer: C — 3

Q. What is the frequency of the function y = sin(2x)?

A. 1/2
B. 1
C. 2
D. 4

Solution

The frequency of y = sin(Bx) is |B|/(2π). Here, B = 2, so the frequency is 2/(2π) = 1/π.

Correct Answer: C — 2

Q. What is the maximum value of the function y = 2cos(3x)?

A. 0
B. 1
C. 2
D. 3

Solution

The maximum value of a cosine function y = Acos(Bx) is |A|. Here, A = 2, so the maximum value is 2.

Correct Answer: C — 2

Q. What is the maximum value of y = -2cos(x)?

A. -2
B. 0
C. 2
D. 4

Solution

The maximum value occurs when cos(x) = -1, giving a maximum of -2 * -1 = 2.

Correct Answer: C — 2

Q. What is the period of the function y = sin(x)?

A. π
B. 2π
C. 3π
D. 4π

Solution

The period of the sine function is 2π.

Correct Answer: B — 2π

Q. What is the period of the sine function?

A. π
B. 2π
C. 3π
D. 4π

Solution

The period of the sine function is 2π, meaning it repeats every 2π units.

Correct Answer: B — 2π

Q. What is the phase shift of y = 4sin(2x + π)?

A. -π/2
B. 0
C. π/2
D. π

Solution

The phase shift is found by setting 2x + π = 0, leading to a shift of -π/2.

Correct Answer: A — -π/2

Q. What is the range of the function y = 2sin(x)?

A. [-2, 2]
B. [-1, 1]
C. [0, 2]
D. (-∞, ∞)

Solution

The range of y = 2sin(x) is [-2, 2] because the sine function oscillates between -1 and 1.

Correct Answer: A — [-2, 2]

Q. What is the range of the function y = 4sin(x)?

A. [-4, 4]
B. [-1, 1]
C. [0, 4]
D. [-2, 2]

Solution

The range of y = Asin(Bx) is [-|A|, |A|]. Here, A = 4, so the range is [-4, 4].

Correct Answer: A — [-4, 4]

Q. What is the value of sin(π/6)?

A. 0
B. 1/2
C. √3/2
D. 1

Solution

The value of sin(π/6) is 1/2.

Correct Answer: B — 1/2

Q. What is the vertical asymptote of y = tan(x)?

A. x = 0
B. x = π/2
C. x = π
D. x = 2π

Solution

The vertical asymptotes of the tangent function occur at x = π/2 + nπ, where n is an integer.

Correct Answer: B — x = π/2

Q. What is the vertical shift of the function y = 5sin(x) + 2?

A. 0
B. 2
C. 5
D. 7

Solution

The vertical shift of the function y = Asin(Bx) + D is D. Here, D = 2, so the vertical shift is 2 units up.

Correct Answer: B — 2

Q. What is the vertical shift of the function y = tan(x) + 2?

A. 0
B. 1
C. 2
D. 3

Solution

The vertical shift is determined by the constant added to the function, which is +2.

Correct Answer: C — 2

Q. What is the x-intercept of the function y = cos(x) - 1?

A. 0
B. π/2
C. π
D. 2π

Solution

The x-intercept occurs when y = 0, which happens at x = 0 for cos(x) - 1.

Correct Answer: A — 0

Q. What is the x-intercept of the function y = cos(x) in the interval [0, 2π]?

A. 0
B. π/2
C. π
D. 3π/2

Solution

The cosine function equals zero at x = π/2 and x = 3π/2. The x-intercepts in [0, 2π] are π/2 and 3π/2.

Correct Answer: C — π

Q. Which of the following is the amplitude of the function y = 3sin(x)?

A. 1
B. 2
C. 3
D. 4

Solution

The amplitude of a sine function y = Asin(Bx) is |A|. Here, A = 3, so the amplitude is 3.

Correct Answer: C — 3

Q. Which of the following is the correct phase shift of y = sin(x - π/4)?

A. 0
B. π/4
C. π/2
D. π

Solution

The phase shift is found by setting the inside of the sine function to zero, giving a shift of π/4 to the right.

Correct Answer: B — π/4

Q. Which of the following represents the phase shift of the function y = sin(x - π/4)?

A. 0
B. π/4
C. π/2
D. π

Solution

The phase shift of y = sin(x - C) is C. Here, C = π/4, so the phase shift is π/4 to the right.

Correct Answer: B — π/4

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