# 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. – starship Feb 7 '11 at 19:38

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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. – starship 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

## 1 Answer

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

Maybe that helps.

Edit: This is just one way, there are many. As asked in the above comments, how are you supposed to solve it? What tools do you have your disposal? What type of things have you being taught so far?

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Ah, that actually helped a lot. Lemme go try and draw it now, to see if it's alright. I'll let you know in a few minutes! ~Brb – starship Feb 7 '11 at 19:49
Oh, I could hug you. It helped so much! Thank you! <3 – starship Feb 7 '11 at 19:52
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