Question

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

Answer 1

We know that,
$y=si{n}^{2}x=\frac{1-cos2x}{2}=\frac{1}{2}-\frac{1}{2}$ cos 2x
We have,
$y=\frac{1}{2}-\frac{1}{2}$ cos =2x
$\Rightarrow y-\frac{1}{2}=-\frac{1}{2}$ cos 2x ...(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
$Y=-\frac{1}{2}$ cos2x.
Thus we draw the grpah of Y=cos2X, 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.