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To obtain the graph of y = 3 sin x we first draw the graph of y = sin x in the interval [0, 2x]. The maximum and minimum values are 3 and - 3 respectively.
We have,
Substituting these values in (i), we get
Y = 2sin x
Thus we draw the graph of Y = 2 sin X and shift it by π/4 to the right to get the required graph.
Y = 2sin 2X
Thus we draw the graph of Y = 2 sin 2X and shift it by 1/2 to the right to get the required graph.
Y = 2sin 3X
Thus we draw the graph of Y = 3 sin 3X and shift it by 1/3 to the right to get the required graph.
Y = 3 sin 2X
Thus we draw the graph of Y = 3 sin 2X and shift it by 1/8 to the right to get the required graph.
Y = sin X.
Thus we draw the graph of Y = sin X and shift it by π/4 to the right to get the required graph.
To obtain the graph of y = sin 3x we first draw the graph of y = sin x in the interval [0, 2π] and then divide the x-coordinates of the points where it crosses x-axis by 3.
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Chapter 6: Graphs of Trigonometric Functions...