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

• Last Updated : 08 May, 2021

### (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. ### (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. ### (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. ### (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. ### (i) y = cos x, y = cos Solution:

Graph 1:

y = cos x 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. The graph y = cos x and are on same axes are as follows: ### (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. 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. The graph y = cos 2x and y = cos are on same axes are as follows: ### (iii) y = cos x, Solution:

Graph 1:

y = cos x 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. The graph y = cos x and y = are on same axes are as follows: My Personal Notes arrow_drop_up
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