Class 11 RD Sharma Solutions – Chapter 6 Graphs of Trigonometric Functions – Exercise 6.2
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:
Last Updated :
08 May, 2021
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