Preparation with RD Sharma Class 11 Solutions Chapter 6
FAQs on RD Sharma Class 11 Solutions Chapter 6 - Graphs of Trigonometric Functions (Ex 6.2) Exercise 6.2
1. What are the key properties like period and amplitude to consider when solving questions in RD Sharma Class 11 Maths Ex 6.2?
When solving problems involving trigonometric graphs in RD Sharma Ex 6.2, you must focus on these key properties:
- Amplitude: The maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position. For y = A sin(x), the amplitude is |A|.
- Period: The interval after which the graph repeats itself. For sin(x) and cos(x), the period is 2π, while for tan(x) it is π.
- Phase Shift: The horizontal shift of the graph from its standard position. For y = sin(x - c), the phase shift is 'c' units.
- Domain and Range: The set of all possible input values (domain) and output values (range) for the function.
Understanding these is crucial for accurately sketching the graphs as required in the exercise solutions.
2. What is the step-by-step method for sketching the graph of a function like y = 3 cos(2x) as per the solutions in Ex 6.2?
To sketch the graph of y = 3 cos(2x) using the method from RD Sharma solutions, follow these steps:
- Step 1: Start with the basic graph of the parent function, which is y = cos(x).
- Step 2: Identify the amplitude. Here, the amplitude is 3, so the graph will be stretched vertically, ranging from -3 to 3.
- Step 3: Calculate the new period. The period of a function y = cos(bx) is 2π/|b|. For this function, the period is 2π/2 = π. This means the graph completes one full cycle in an interval of π radians.
- Step 4: Plot key points (maxima, minima, and zero-crossings) within one period (from 0 to π) and then repeat the pattern.
3. Why is understanding the phase shift crucial when solving problems on trigonometric graphs in RD Sharma Ex 6.2?
Understanding the phase shift is crucial because it determines the starting point of the trigonometric cycle. A phase shift moves the entire graph horizontally along the x-axis without changing its shape, amplitude, or period. For a function like y = sin(x - c), a positive 'c' shifts the graph to the right, and a negative 'c' (as in y = sin(x + c)) shifts it to the left. Accurately identifying the phase shift is essential for plotting the correct position of the graph, which is a common requirement in the problems of Exercise 6.2.
4. What is a common mistake to avoid when graphing a function with a phase shift, for example, y = sin(x - π/2)?
A very common mistake is shifting the graph in the wrong direction. For the function y = sin(x - π/2), the term '-π/2' indicates a phase shift to the right by π/2 units, not to the left. Students often incorrectly associate the minus sign with a leftward shift. The RD Sharma solutions help clarify this by demonstrating the transformation from the parent graph y = sin(x) step-by-step, ensuring you start the cycle at the correct point on the x-axis.
5. How does the graph of y = cos(x) differ from y = cos|x|?
There is no difference between the graphs of y = cos(x) and y = cos|x|. This is because the cosine function is an even function, which means that cos(-x) = cos(x) for all values of x. Since the function's value is the same for both positive and negative inputs, reflecting the positive x-axis part of the graph onto the negative x-axis (which is what y = f|x| does) results in the exact same graph as the original y = cos(x).
6. How does changing the 'b' value in y = sin(bx) affect the graph's frequency as explained in Chapter 6?
The value of 'b' in y = sin(bx) directly controls the period and frequency of the graph. The period is calculated as 2π/|b|. A larger 'b' value results in a smaller period, causing the graph to oscillate more rapidly. This means the function has a higher frequency (more cycles in a given interval). Conversely, a smaller 'b' value (between 0 and 1) results in a longer period, stretching the graph horizontally and leading to a lower frequency.
7. How do the RD Sharma solutions for Chapter 6 help build a strong foundation for exams?
The chapter on trigonometric graphs is fundamental for both Class 11 exams and competitive entrance exams like JEE. The RD Sharma solutions for Exercise 6.2 offer a comprehensive set of problems that go beyond the NCERT textbook, helping you master concepts like amplitude, period, and phase shift transformations. By practising these detailed, step-by-step solutions, you develop the ability to accurately sketch and interpret any graphical transformation question, which is a high-value skill for exams.
8. Where can I find accurate and easy-to-understand solutions for all questions in RD Sharma Class 11 Maths Chapter 6, Exercise 6.2?
Vedantu provides detailed, step-by-step solutions for every problem in RD Sharma Class 11 Maths Ex 6.2. These solutions are prepared by subject matter experts to align with the CBSE 2025-26 syllabus and are designed to be easy to follow. They ensure you understand the correct method for sketching trigonometric graphs and can solve problems accurately for your school exams.
