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Question

Sketch the graph of the following pairs of function on the same axes:

(i) y=sin x, y=sin x+π4
(ii) y = sin x, y = sin 3x

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Solution

(i)
First, we draw the graph of y = sin x.
Then, let us draw the graph of y=sinx+π4.
y=sinx+π4 y-0=sinx+π4 ...(i)On shifting the origin at -π4,0, we get:x=X-π4 and y=Y+0On subsitituting the values in (i), we get:Y=sinXThen, we draw the graph of Y=sinX and shift it by π4 to the left.
Then, we will obtain the following graph:


(ii)
First, we draw the graph of y = sin x.
Let us now draw the graph of y = sin 3x.
Step I- We find the value of c and a by comparing y = sin 3x with y = c sin ax, i.e. c = 1 and a =3.
Step II - Then, we draw the graph of y = sin x and mark the point where it crosses the x-axis.
Step III - Divide the x-coordinates of the points where y = sin x crosses x-axis by 3 (i.e. a =3) and mark the maximum value (i.e. c = 1) and minimum value (i.e.-c = -1).
Then, we obtain the following graph:

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