### Sketch the graphs of the following functions:

### Question 1: y = sin^{2} x

**Solution:**

As we know that,

y = sin

^{2}x =On shifting the origin at (0, 1/2), we get

X = x and Y =

On substituting these values, we get

The maximum and minimum values of Y are and respectively and shift it by 1/2 to the up.

As the equation in the form of y = – f(x), the graph become inverted of y = f(x)

### Question 2: y = cos^{2} x

**Solution:**

As we know that,

y = cos

^{2}x =On shifting the origin at , we get

X = x and Y =

On substituting these values, we get

The maximum and minimum values of Y are and respectively and shift it by 1/2 to the up.

### Question 3: y = sin^{2}

**Solution:**

To obtain this graph y-0 = sin

^{2}On shifting the origin at (,0), we get

X = and Y = y – 0

On substituting these values, we get

Y = sin

^{2}XFirst we draw the graph of Y = sin

^{2}X and shift it by π/4 to the right.

### Question 4: y = tan 2x

**Solution:**

To obtain this graph y = tan 2x,

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

### Question 5: y = 2 tan 3x

**Solution:**

To obtain this graph y = 2 tan 3x,

First we draw the graph of y = tan x and then divide the x-coordinates of the points where it crosses x-axis by 3.

Stretch the graph vertically by the factor of 2.

### Question 6: y = 2 cot 2x

**Solution:**

To obtain this graph y = 2 cot 2x,

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

Stretch the graph vertically by the factor of 2.

### Sketch the graphs of the following functions on the same scale:

### Question 7: y = cos ^{2}x, y = cos

**Solution:**

Graph 1:y = cos

^{2}xAs we know that,

y = cos

^{2}x =On shifting the origin at (0, 1/2), we get

X = x and Y =

On substituting these values, we get

The maximum and minimum values of Y are and respectively and shift it by 1/2 to the up.

Graph 2:To obtain this graph y-0 = cos (2x-) = cos 2(x-)

On shifting the origin at (π/6, 0), we get

X = and Y = y – 0

On substituting these values, we get

Y = cos 2X

First we draw the graph of Y = cos 2X and shift it by π/6 to the right.

The graph y = cos

^{2}x and y = cos are on same axes are as follows:

### Question 8: y = sin^{2} x, y = sin x

**Solution:**

Graph 1:y = sin

^{2}xAs we know that,

y = sin

^{2}x =On shifting the origin at (0, ), we get

X = x and Y =

On substituting these values, we get

The maximum and minimum values of Y are and respectively and shift it by 1/2 to the up.

As the equation in the form of y = – f(x), the graph become inverted of y = f(x)

Graph 2:y = sin x

The graph y = sin

^{2}x and y = sin x are on same axes are as follows:

### Question 9: y = tan x, y = tan ^{2}x

**Solution:**

Graph 1:y = tan x

Graph 2:y = tan

^{2}xThe graph y = tan x and y = tan

^{2}x are on same axes are as follows:

### Question 10: y = tan 2x, y = tan x

**Solution:**

Graph 1:To obtain this graph y = tan 2x,

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

Graph 2:y = tan x

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