Preparation with RD Sharma Class 11 Solutions Chapter 6 - Free PDF
FAQs on RD Sharma Class 11 Solutions Chapter 6 - Graphs of Trigonometric Functions (Ex 6.3) Exercise 6.3
1. How do Vedantu's RD Sharma Solutions for Class 11 Maths Ex 6.3 help in solving problems correctly?
Vedantu's solutions for RD Sharma Class 11 Maths Exercise 6.3 provide a reliable, step-by-step methodology for each problem. They are designed by subject matter experts to align with the CBSE 2025-26 syllabus, ensuring you learn the correct approach to graph trigonometric functions. Following these solutions helps in understanding how to apply transformations like changes in amplitude, period, and phase shift, which is crucial for scoring well in exams.
2. What is the primary focus of the problems in RD Sharma Class 11 Maths Exercise 6.3?
The primary focus of Exercise 6.3 in RD Sharma's Class 11 Maths Chapter 6 is on graphing transformations of trigonometric functions. The questions require you to accurately plot functions of the form y = A f(Bx + C), where f(x) is a basic trigonometric function like sin(x) or cos(x). The exercise tests your ability to correctly identify and apply the effects of amplitude, period, and phase shift on the standard graphs.
3. What is the correct step-by-step method to solve questions on plotting transformed trigonometric functions in Ex 6.3?
To accurately solve problems on graphing transformed trigonometric functions, follow this methodical approach:
Identify the Base Function: Determine the basic trigonometric function, such as sin(x), cos(x), or tan(x).
Find Key Parameters: From the given equation, calculate the amplitude, determine the new period (e.g., 2π/|B| for sine), and find the phase shift (-C/B).
Sketch the Base Graph: Lightly draw the graph of the base function over one period.
Apply Transformations: Sequentially apply the calculated phase shift (horizontal shift), amplitude change (vertical stretch/compression), and any vertical shifts to the base graph to arrive at the final, accurate plot.
4. When graphing functions like y = A sin(Bx + C), what is a common mistake students make, and how can it be avoided?
A very common mistake is misinterpreting the phase shift. Students often incorrectly assume the horizontal shift is just 'C'. The correct phase shift is actually -C/B. To avoid this error, always rewrite the function by factoring out B from the argument. The expression becomes y = A sin(B(x + C/B)). This form clearly shows that the graph is shifted horizontally by -C/B units, preventing a fundamental error in plotting the function's position.
5. Why is determining the correct period of a trigonometric function a crucial first step for problems in RD Sharma Chapter 6?
Determining the correct period is crucial because it defines the fundamental interval over which the function's entire pattern repeats. If the period is calculated incorrectly (for instance, using 2π for a tangent function whose period is π), the resulting graph will be stretched or compressed incorrectly, leading to a completely wrong representation. Calculating the correct period (e.g., 2π/|B| for sine/cosine) ensures you accurately draw one full cycle, which can then be repeated to show the complete periodic nature of the function.
6. How can understanding the graph of y = cos(x) help in correctly plotting the graph of y = sec(x)?
Understanding the graph of y = cos(x) provides a direct method for plotting its reciprocal, y = sec(x). The process is as follows:
First, lightly sketch the graph of y = cos(x).
The x-intercepts of the cos(x) graph (where cos(x) = 0) become the locations of the vertical asymptotes for the sec(x) graph, since sec(x) is undefined at these points.
The maximum points of cos(x) (at y=1) become the minimum points of the upward-opening parabolas of sec(x). Similarly, the minimum points of cos(x) (at y=-1) become the maximum points of the downward-opening parabolas of sec(x).
7. What foundational topics from Chapter 6 must be mastered before attempting Exercise 6.3?
Before attempting Exercise 6.3, a student must have a solid understanding of the basic graphs of all six trigonometric functions as per the NCERT syllabus. Key concepts include:
The shape, domain, range, and period of y = sin(x) and y = cos(x).
The characteristics and asymptotes of y = tan(x) and y = cot(x).
The relationship and graphical properties of the reciprocal functions: y = csc(x) and y = sec(x).
Mastering these fundamentals is essential for applying the transformations taught in Exercise 6.3.
