Sketch the graph of the following functions on the same scale :
$y = c o s 2 x, y = c o s (2 x - \frac{π}{3})$

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Solution

We have,
$y = c o s 2 (x - \frac{π}{6})$
$\Rightarrow y - 0 = c o s 2 (x - \frac{π}{6})$ ...(i)
Shifting the origin at $(\frac{π}{6}, 0)$ , we obtain
$x - X + \frac{π}{6}, y = Y + 0$
Substituting these values in (i), we get
Y=cos 2X.
Thus we draw the graph of Y= cos 2x and shift it by $\frac{π}{6}$ to right to get the required graph.

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