Chapter 13.5, Problem 1OE

To determine

The graph of the equation $y={\sin }^{2}x$ using the given equation.

Explanation of Solution

Given information:

The given equation is $\cos 2x=1-2{\sin }^{2}x.$

Calculations:

Here the equation number is $\cos 2x=1-2{\sin }^{2}x.$ .

Simplifying the equation we set,

  $\begin{array}{l}\cos 2x=1-2{\sin }^{2}x.\\ 2{\sin }^{2}x.=1-\cos 2x\\ {\sin }^{2}x=\frac{1}{2}(1-\cos 2x)\end{array}$

Now we can write the equation,

  $y={\sin }^{2}x$ ,as

  $y=\frac{1}{2}(1-\cos 2x)$

Now we draw the graph.