Question

Sketch the graph of the following functions:
$y=si{n}^2(x-\frac{\pi }{4})$

Answer 1

We know that,
$y=si{n}^2(x-\frac{\pi }{4})$
$\Rightarrow y-0=si{n}^2(x-\frac{\pi }{4})$ ...(i)
Shifting the origin at $(\frac{\pi }{4},0)$, we obtain
$x=X+\frac{\pi }{4},y=Y+0$
Substituting these values in (i), we get
$Y=si{n}^{2}X$.
Thus we draw the graph of $Y=si{n}^{2}X$, and shift it by $\frac{\pi }{4}$ to the right to get the required graph.