Question

Sketch the graph of the following functions :
$y=co{s}^{2}x$

Answer 1

We know that,
$y=co{s}^{2}x=\frac{1+cos2x}{2}=\frac{1}{2}+\frac{1}{2}cos2x$
We have,
$y=\frac{1}{2}+\frac{1}{2}cos=2x$
$\Rightarrow y-\frac{1}{2}=\frac{1}{2}cos2x$ ...(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= - $\frac{1}{2}$ 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 $\frac{1}{2}$ down to get the required graph.