Special Identities - troubles rationalizing

**tiar** · November 3rd 2008, 04:32 PM

I'm currently studying for my upcoming precalculus midterm, but I'm having troubles rationalizing denominators and simplifying--and I'm not sure if I'm approaching this correctly. If anyone could lend me pointers to simplify please let me know, I'm really weak in this area.

Use a sum or difference formula to find the exact value of the given expression:

$\sin \frac{7\pi}{12}$
I figured...
$\frac{\pi}{4} + \frac{\pi}{3}=\frac{7\pi}{12}$
Thus according to the values...
$\frac{\sqrt2}{2}\times\frac{\sqrt2}{2}+\frac{\sqrt 3}{2}\times\frac{1}{2}$

I totally got the wrong answer from here. How should I go about simplifying this?

**Jameson** · November 3rd 2008, 06:01 PM

So we have $\frac{\sqrt2}{2}\times\frac{\sqrt2}{2}+\frac{\sqrt 3}{2}\times\frac{1}{2}$

Order of operations says multiply before adding so let's multiply everything together we can.

$\frac{\sqrt{2}*\sqrt{2}}{2*2}+\frac{\sqrt{3}*1}{2* 2}$

$\frac{2}{4}+\frac{\sqrt{3}}{4} = \frac{2+\sqrt{3}}{4}$

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