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Question

Sketch the following graphs :
(i) y=2 sin 2x
(ii) y= 3 sin x
(iii) y=2sin(xπ4)
(iv) y=2 sin (2x-1)
(v) y=3 sin(3x+1)
(vi) y=3sin(2xπ4)

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Solution

(i)To obtain the graph of y = 2sin 2x we first draw the graph of y = sinx in the interval [0,2x] and then divide the x-coordinates of the points where it crosses x-axis by 2. The maximum and minimum values are 2 and -2 respectively.


(ii) To obtain the graph of y=3sin x we first draw the graph of y=sinx in the interval [0,2π]. The maximum and minimum values are 3 and -3 respectively.


(iii) We have
y=2 sin (xπ4)
(y0)=2 sin (xπ4)
Shifting the origin at (π4,0), we have
x=X+π4andy=Y+0
Substituting these values in (i), we get
Y=2 sin X
Thus we draw the graph of Y=2 sin X and shift it by π4to the right to get the required graph.


(iv) We have,
y=2 sin (2x-1)
(y0)=2 sin 2(x12)
Shifting the origin at (12), we have
x=X+12andy=Y+0
Substituing these values in (i), we get
Y=2 sin 2 x
Thus we draw the graph of Y=2 sin 2x and shift it by 12to the right to get the requuired graph.


(v) We have,
y=3 sin (3x+1)
(y0)=3 sin 3(x+13)
Shifting the origin at (13,0), we have x=X-13 and y = Y+0
Substituting these values in (i), we get
Y=3 sin 3X
Thus we draw the graph of Y=3 sin 3X and shift it by 13to the left to get the required graph.


(vi) We have,
y=3 sin (2xπ4)
(y0)=3sin2(xπ8)
Shifting the origin at (π8,0), we have
x = X + π8 and y=Y+0
Substituting these values in (i), we get Y=3 sin 2X
Thus we draw the graph of Y=3 sin 2X and shift it by π8 to the right to get the required graph.


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