Open in App
Not now

# 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
Related Articles