Class 11 RD Sharma Solutions - Chapter 6 Graphs of Trigonometric Functions - Exercise 6.2

Question 1: Sketch the following graphs:

(i) y = cos (x+)

Solution:

To obtain this graph y-0 = cos (x+),

Shifting the origin at , we have

X = x+ and Y = y-0

Substituting these values, we get

Y = cos X

First we draw the graph of Y = cos X and shift it by  to the left.

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(ii) y = cos (x-)

Solution:

To obtain this graph y-0 = cos (x-),

Shifting the origin at , we have

X =  and Y = y-0

Substituting these values, we get

Y = cos X

First we draw the graph of Y = cos X and shift it by  to the right.

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(iii) y = 

Solution:

To obtain this graph y-0 = 3 cos 2(x-),

Shifting the origin at , we have

X =  and Y = y-0

Substituting these values, we get

Y = 3 cos 2X

First we draw the graph of Y = 3 cos 2X and shift it by  to the right.

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

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(iv) 

Solution:

To obtain this graph y-0 = ,

Shifting the origin at , we have

X =  and Y = y-0

Substituting these values, we get

Y = 2 cos X

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

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

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Question 2: Sketch the graphs of the following functions on the same scale:

(i) y = cos x, y = cos 

Solution:

Graph 1:

y = cos x

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Graph 2:

To obtain this graph y-0 = cos ,

Shifting the origin at , we have

X =  and Y = y-0

Substituting these values, we get

Y = cos X

First we draw the graph of Y = cos X and shift it by  to the right.

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The graph y = cos x and  are on same axes are as follows:

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(ii) y = cos 2x, y = cos 

Solution:

Graph 1:

To obtain this graph y = cos 2x,

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

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Graph 2:

To obtain this graph y-0 = cos ,

Shifting the origin at , we have

X =  and Y = y-0

Substituting these values, we get

Y = cos 2X

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

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The graph y = cos 2x and y = cos are on same axes are as follows:

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(iii) y = cos x, 

Solution:

Graph 1:

y = cos x

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Graph 2:

To obtain this graph y = ,

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

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The graph y = cos x and y =  are on same axes are as follows:

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