Chapter 13.4, Problem 47WE

To determine

To Show: The graph $y=\sin x\cos x$ is a sine curve. Sketch the graph.

Explanation of Solution

Given:Use the equation $\sin 2x=2\sin x\cos x$ .

Given: $\sin 2x=2\sin x\cos x$

Draw the graph of $\sin xand\cos x$ .

  

Now graph the function $y=\sin x\cos x$

  

We see that the graph is similar to the $\sin$ graph.

The period of the function $y=\sin x\cos x$ is $\pi$ .

The amplitude is $\frac{1}{2}$

Thus

We can write the function in terms of sine function.

  $\sin x\cos x=\frac{1}{2}\sin 2x$