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We have,
Substituting these values in (i), we get
Y = cost X.
Thus we draw the graph of Y = cos X and shift it by π/4 to the left to get the required graph.
Y = cos X.
Y = 3 cos 2X.
Thus we draw the graph of Y = 3 cos 2 X and shift it by 1/2 to the left to get the required graph.
Y = 2 cos X.
Thus we draw the graph of Y = 2 cos X and shift it by π/2 to the left to get the required graph.
Y = cos 2X.
Thus we draw the graph of Y = 2 cos X and shift it by π/4 to the left to get the required graph.
To obtain the graph of y = cos x/2 we first draw the graph of y = cos x in the interval [0, 2π] and then divide the x-coordinates of the points where it crosses x-axis by 1/2.
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Chapter 6: Graphs of Trigonometric Functions...