Chapter 6: Graphs of Trigonometric Functions – Exercise 6.3
Graphs of Trigonometric Functions – Exercise 6.3 – Q.1
We know that
We have,
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Substituting these values in (i), we get
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Thus we draw the graph of Y = cos 2X, adjust the maximum and minimum values to 1/2 and -1/2 and shift it by 1/2 up to get the required graph.
Graphs of Trigonometric Functions – Exercise 6.3 – Q.2
We know that
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We have,
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Substituting these values in (i), we get
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Thus we draw the graph of Y = cos 2X, adjust the maximum and minimum values to 1/2 and -1/2 and shift it by 1/2 up to get the required graph.
Graphs of Trigonometric Functions – Exercise 6.3 – Q.3
We have,
Substituting these values in (i), we get
Y = sin2X.
Thus we draw the graph of Y = sin2 X, and shift it by π/4 to the rught to get the required graph.
Graphs of Trigonometric Functions – Exercise 6.3 – Q.4
To obtain the graph of y = tan 2x we first draw the graph of y = tan x in the interval 
and then divide the x-coordinates of the points where it crosses x-axis by 2.
Graphs of Trigonometric Functions – Exercise 6.3 – Q.5
To obtain the graph of y = tan 3x we first draw the graph of y = tan x in the interval
and then divide the x-coordinates of the points where it crosses x-axis by 3. We then stretch the graph vertically by a factor of 2.
Graphs of Trigonometric Functions – Exercise 6.3 – Q.6
To obtain the graph of y = 2 cot 2x we first draw the graph of y = cot x in the interval (0, π) and then divide the x-coordinates of the points where it crosses x-axis by 2. We then stretch the graph vertically by a factor of 2.
Graphs of Trigonometric Functions – Exercise 6.3 – Q.7
We have,
Substituting these values in (i), we get
Y = cos 2X.
Thus we draw the graph of Y = cos 2X, and shift it by π/6 to the rught to get the required graph.
Graphs of Trigonometric Functions – Exercise 6.3 – Q.8
We know that
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We have,
Thus we draw the graph of Y = cos 2X, adjust the maximum and minimum values to 1/2 and -1/2 and shift it by 1/2 up to get the required graph.
