### Question 1. Sketch the following graphs:

### (i) y = 2 sin 2x

**Solution:**

To obtain this graph y = 2 sin 2x,

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)

**Solution:**

To obtain this graph y-0 = ,

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

X = 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 ,

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

X = 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,

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

X = 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)

To obtain this graph y-0 =

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

X = 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,

Graph 1:y = sin x

Graph 2:To obtain this graph y-0 =

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

X = 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 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: