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: