### 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.

### (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.

### 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

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: