Sketch the graph of the following pairs of functions on the same axes:
(i) y=sin x, y = sin $(x + \frac{π}{4})$
(ii) y=sin x, y = sin 3x

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Solution

(i) y= sin $(x + \frac{π}{4})$
$\Rightarrow y - 0 = s i n (x + \frac{π}{4})$ ....(i)
Shifting the origin at $(- \frac{π}{4}, 0)$ , we obtain
$x = X - \frac{π}{4}, y = Y + 0$
Substituting these values in (i), we get Y= sin X.
Thus we draw the graph of Y=sin X and shift it by $\frac{π}{4}$ to the left to get the required graph.

(ii) To obtain the graph of y = sin 3x we frist draw the grpah of y = sin x in the interval $[0, 2 π]$ and then divide the x - coordinates of the points where it crosses x-axis by 3.

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Sketch the graph of the following pairs of functions on the same axes: (i) y=sin x, y = sin (x+π4) (ii) y=sin x, y = sin 3x

Sketch the graph of the following pairs of functions on the same axes:
(i) y=sin x, y = sin $(x + \frac{π}{4})$
(ii) y=sin x, y = sin 3x