Detailed solutions for RD Sharma Class 11 Maths Chapter 6: Graphs of Trigonometric Functions are provided here for students’ exam preparation. In the previous chapters, students learned about periodic properties of trigonometric functions. In this chapter, students will explore how to plot the graphs of these functions over intervals equal to their respective periods.
To support students in performing well in their Class 11 Maths exams, these solutions follow the latest CBSE syllabus and present exercise-wise problems solved step by step for better understanding. Students are encouraged to regularly practice these solutions to strengthen their conceptual clarity and improve their exam performance.
Introduction to Class 11 Maths Chapter 6: Graphs of Trigonometric Functions – Solutions
Chapter 6 consists of three exercises covering the following key concepts:
- Graph of the sine function
- Graph of the cosine function
- Graph of the tangent function
- Graph of the cosecant function
- Graph of the cotangent function
- Graph of the secant function
These solutions are available for study both online and offline, ensuring flexible learning as per students’ convenience. Regular practice with these solved examples will help students develop a strong foundation in trigonometric graphs.
RD Sharma Solutions Class 11 Maths Chapter 6 - Graphs of Trigonometric Functions Question with Answers
- What is the period of the sine function?
Answer: The period of the sine function, sin(x), is 2π. - What is the amplitude of the cosine function?
Answer: The amplitude of cos(x) is 1. - At what points does sin(x) become zero?
Answer: sin(x) = 0 at x = nπ, where n is any integer. - What is the range of sin(x)?
Answer: The range of sin(x) is [-1, 1]. - Write the general shape of the sine function graph.
Answer: The sine graph is a smooth, continuous wave (sinusoidal) oscillating between -1 and 1. - At what points is cos(x) equal to zero?
Answer: cos(x) = 0 at x = (2n + 1)π/2. - What is the period of the tangent function?
Answer: The period of tan(x) is π. - Does the tangent function have asymptotes?
Answer: Yes, it has vertical asymptotes at x = (2n + 1)π/2. - What is the range of the tangent function?
Answer: (-∞, ∞). - What is the period of cosecant (csc x)?
Answer: The period is 2π. - At which points is cosecant function undefined?
Answer: x = nπ, where sin(x) = 0. - What is the minimum value of cos(x)?
Answer: -1. - Which trigonometric functions have vertical asymptotes?
Answer: tan(x), cot(x), sec(x), cosec(x). - What is the domain of sec(x)?
Answer: R – { (2n + 1)π/2 }. - At which points does sec(x) intersect the y-axis?
Answer: At x = 0, sec(0) = 1. - Which trigonometric function is even?
Answer: cos(x) and sec(x). - Which trigonometric function is odd?
Answer: sin(x), tan(x), cot(x), and cosec(x). - What is the range of sec(x)?
Answer: (-∞, -1] ∪ [1, ∞). - How many cycles does sin(x) complete in [0, 4π]?
Answer: 2 cycles. - At what x-values is tan(x) zero?
Answer: x = nπ. - At what points is cot(x) undefined?
Answer: x = nπ, where sin(x) = 0. - What is the period of cot(x)?
Answer: π. - Where does sin(x) start and end within [0, 2π]?
Answer: Starts at 0, peaks at 1 at π/2, drops to -1 at 3π/2, and returns to 0 at 2π. - Is cos(x) a phase shift of sin(x)?
Answer: Yes, it leads by π/2. - What is the relation between sec(x) and cos(x)?
Answer: sec(x) = 1/cos(x) and is undefined where cos(x) = 0.
RD Sharma Class 11 Maths Chapter 6: Graphs of Trigonometric Functions – Download PDF
Frequently Asked Questions
Chapter 6 focuses on the Graphs of Trigonometric Functions. It explains how to draw graphs of standard trigonometric functions like sin(x), cos(x), tan(x), cot(x), sec(x), and cosec(x), including their periodic nature, amplitude, range, and points of intersection with axes.
There are three exercises in Chapter 6. Each exercise deals with graphing different trigonometric functions and understanding their unique properties.
Trigonometric graphs help students visualize the behavior of trigonometric functions, understand their periodicity, amplitude, and points of discontinuity (asymptotes). This understanding is useful in advanced topics like calculus, physics, and engineering.
Chapter 6 includes:
- Graph of sine (sin x)
- Graph of cosine (cos x)
- Graph of tangent (tan x)
- Graph of cosecant (cosec x)
- Graph of secant (sec x)
- Graph of cotangent (cot x)
The period of both sine and cosine functions is 2π, meaning their graphs repeat after every 2π interval.
Yes. The graphs of tan(x) and cot(x) have vertical asymptotes and their period is π. They are unbounded, meaning they extend to positive and negative infinity, unlike sine and cosine which are bounded between -1 and 1.
Yes. The step-by-step RD Sharma solutions help students learn graph plotting techniques easily, which are frequently tested in Class 11 exams and are foundational for Class 12 and competitive exams like JEE
You can download RD Sharma Chapter 6 solutions from popular educational platforms like Infinity Learn, Vedantu, BYJU'S, or from CBSE guide websites in PDF format for easy access.