# Graph for $f(x)=\sin x\cos x$

Okay, so in my math homework I'm supposed to draw a graph of the following function: $$f(x)=\sin x \cos x.$$ I have the solution in the textbook, but I just can't figure out how they got to that. So, if someone could please post (a slightly more detailed) explanation for this, it would be really appreciated.

I have to turn the homework this Wednesday, but since I already have the solution the answer doesn't have to be really swift. Bonus points if it is, tohugh

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What are the tools have at your disposal? In other words: you say this is a math homework. Is this for a calculus course, a pre-calculus course, a geometry course, a trigonometry course? The answer will depend on what tools you are expected to use. – Arturo Magidin Feb 7 '11 at 19:31
I'd say it's trigonometry, but I'm not 100% sure. We don't categorise courses like that here. – omninonsense Feb 7 '11 at 19:38
What are the tools you are expected to use? Derivatives? Geometry? Knowledge about what sine and cosine look like? Trigonometric identities? Some or all of the above? Really: the answer depends entirely on what tools you have at your disposal. If you are expected to use calculus (derivatives), then you have one approach; if you don't know calculus, then the approach is different. – Arturo Magidin Feb 7 '11 at 19:40
Geometry. We didn't learn Derivatives, yet (we're doing that next year). And we're expected to know what since and cosine look like. – omninonsense Feb 7 '11 at 19:45
Then Eric's answer is almost certainly the intended answer: use some trigonometric identities to get the function you want into an easier form, and then do the graph of that easier form. You should know what the graph of $\sin(2x)$ is, based on the graph of $y=\sin x$, and then how to go from the graph of $y=\sin 2x$ to $y=\frac{1}{2}\sin 2x$. – Arturo Magidin Feb 7 '11 at 19:50

Here is a hint: Can you draw the graph of $\sin x$? What about $a\sin{(bx)}$? Then recall the identity $$\sin{x} \cos{x} = \frac{1}{2} \sin {2x}.$$