Question

Sketch the graph of the following functions:
y= $si{n}^2$ x,y = sin x

Answer 1

We know that
$y=si{n}^{2}x=\frac{1-cos2x}{2}=\frac{1}{2}-\frac{1}{2}$ cos2x We have,
$y=\frac{1}{2}-\frac{1}{2}cos2x$
$\Rightarrow y-\frac{1}{2}=-\frac{1}{2}cos2x$ ...(i)
Shifting the origin at $(0,-\frac{1}{2})$, we obtain
$x-X,y=Y+\frac{1}{2}$
Substituting these values in (i), we get
Y= - $\frac{1}{2}$cos 2X.
Thus we draw the graph of Y= cos 2x, adjust the maximum and minimum values to $\frac{1}{2}$ and - $\frac{-1}{2}$ and shift it by $\frac{1}{2}$ up to get the required graph.