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: