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I tried to continue my homework but ran into another problem I couldn't do, literally can't continue now.

I have to graph $\displaystyle y=\frac 32 \sin2\left(x+ \frac{\pi}{4}\right)$

What do I do with $\sin 2$? Is it $\sin(2x + \pi/2)$, $\sin4(x/2 + \pi/8)$ or what?

Edit: I've got that the period of the function is $\pi$.

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    Check if your answer is correct with [Wolfram](http://www.wolframalpha.com/input/?i=y+%3D+3%2F2*sin%282x%2B%CF%80%2F2%29). It's useful to note that $\sin 2(x + \pi/4) = \sin (2x + \pi/2) = \cos 2x$.2011-06-13

2 Answers 2

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Based on what you give lower down, you want to graph $y=\frac {3}{2} \sin (2(x+\frac{\pi}{4}))$. Both your expansions are correct. To determine the period, how much does $x$ have to increase to make the argument of the sine function (the stuff in the parentheses) increase by $2\pi$? Both your expansions should give the same answer to that question.

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    If I interpreted it correctly, you are right that $\pi$ is the period. The period is also $\pi$ if it is $\frac{3}{2} \sin^2 (x + \frac{\pi}{4})$, but the graph looks different.2011-06-13
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If the question is not clear, you should ask your teacher to clarify it. We can't read the teacher's mind - we can't even see the original question, just your transcription of it. I rather suspect that it should be $\frac{3}{2} \sin^2 (x + \frac{\pi}{4})$, that is, (3/2) * (sin(x+pi/4))^2, but that's only a guess. It might be $\frac{3}{2} \sin(2(x+\frac{\pi}{4}))$.

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    @Adam: You are unlikely to get the right answer unless you work on the right problem. We had this issue on your last question as well-you need to know whether you have $\sin 2\theta$ or $\sin^2\theta$. The way you write it is not clear. If it is not clear in your notes, you are in trouble.2011-06-13