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Class 11 RD Sharma Solutions – Chapter 6 Graphs of Trigonometric Functions – Exercise 6.1

  • Last Updated : 30 Apr, 2021

Question 1. Sketch the following graphs:

(i) y = 2 sin 2x

Solution:

To obtain this graph y = 2 sin 2x,

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First we draw the graph of y = sin x and then divide the x-coordinates of the points where it crosses x-axis by 2.



The maximum and minimum values of y are 2 and -2 respectively.

(ii) y = 3 sin x

Solution:

To obtain this graph y = 3 sin x,

First we draw the graph of y = sin x.

The maximum and minimum values of y are 3 and -3 respectively.



(iii) y = 2 \hspace{0.1cm}sin (x-\frac{\pi}{4})

Solution:

To obtain this graph y-0 = 2 \hspace{0.1cm}sin (x-\frac{\pi}{4}) ,

On shifting the origin at (π/4, 0), we get

X = x-\frac{\pi}{4}  and Y = y – 0

On substituting these values, we get

Y = 2 sin X

First we draw the graph of Y = 2 sin X and shift it by π/4 to the right.

(iv) y = 2 sin (2x – 1)

Solution:



To obtain this graph y – 0 = 2 sin 2(x-\frac{1}{2}) ,

On shifting the origin at (1/2, 0), we get

X = x-\frac{1}{2}  and Y = y – 0

On substituting these values, we get

Y = 2 sin 2X

First we draw the graph of Y = 2 sin 2X and shift it by 1/2 to the right.

(v) y = 3 sin (3x + 1)

Solution:

To obtain this graph y – 0 = 3 sin 3(x+\frac{1}{3}) ,

On shifting the origin at(-1/3, 0), we get



X =  x+\frac{1}{3}  and Y = y – 0

On substituting these values, we get

Y = 3 sin 3X

First we draw the graph of Y = 3 sin 3X and shift it by 1/3 to the left.

(vi) y = 3 \hspace{0.1cm}sin (2x-\frac{\pi}{4})

To obtain this graph y-0 = 3 \hspace{0.1cm}sin \hspace{0.1cm}2(x-\frac{\pi}{8}),

On shifting the origin at (π/8, 0), we get

X = x-\frac{\pi}{8}  and Y = y-0

On substituting these values, we get

Y = 3 sin 2X



First we draw the graph of Y = 3 sin 2X and shift it by π/8 to the right.

Question 2: Sketch the graph of the following pairs of functions on the same axes:

(i) y = sin x, y = sin (x+\frac{\pi}{4})

Graph 1:

y = sin x

Graph 2:

To obtain this graph y-0 = sin (x+\frac{\pi}{4}),

On shifting the origin at (-π/4, 0), we get

X = x+\frac{\pi}{4}  and Y = y – 0

On substituting these values, we get

Y = sin X

First we draw the graph of Y = sin X and shift it by π/4 to the left.

The graph y = sin x and y = sin (x+\frac{\pi}{4})  are on different axes are as follows:

(ii) y = sin x, y = sin 3x

Graph 1:

y = sin x

Graph 2:

To obtain this graph y = sin 3x,

First we draw the graph of y = sin x and then divide the x-coordinates of the points where it crosses x-axis by 3.

The graph y = sin x and y = sin 3x are on different axes are as follows:




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