what is the exact answer for sin(3pi/4 + 5pi/6)??

Question

accessdenied · Answer

Have you tried using sine's angle-sum formula to split this in terms of the two nice angles you can find on unit circle?

anonymous · Answer

I am having a hard time understanding how to use it. Ive tried but my answers dont work

accessdenied · Answer

The angle sum formula of sine is:
    $ \sin (\alpha + \beta) = \sin \alpha \cos \beta + \sin \beta \cos \alpha $
You have this formula?
We would just have to substitute the two angles for $\alpha$ and $\beta$ there.  The formula is always true when we substitute.

anonymous · Answer

ive tried but my answer was wrong

accessdenied · Answer

What answer did you get?

anonymous · Answer

(-sqr6-sqr2)/4

anonymous · Answer

$$\frac{ -\sqrt{6}-\sqrt{2}}{4}$$

accessdenied · Answer

Hm.  Is this being done through something online or do you have an actual answer to compare to?  (I got the same thing, but maybe it wants a different format)

anonymous · Answer

i did the approx of that answer and the question and they are different

accessdenied · Answer

Oh.  You compared the value of Sine(3pi/4 + 5pi/6) to the approx of the answer obtained?
If so, maybe you should check the calculation again.  Especially if a calculator is in radians or degrees, that is sometimes a really good trip-up.

anonymous · Answer

its in radians dont worry about that

anonymous · Answer

i got the same thing
$$\frac{ -\sqrt{6}-\sqrt{2} }{ 4 }$$

accessdenied · Answer

correct parentheses too?
  [ -sqrt(6) - sqrt(2) ]/4
if you only have  -sqrt(6) - sqrt(2)/4, it only divides the sqrt(2) by 4.

anonymous · Answer

unless he has to leave it as the difference of 2 fractions?

anonymous · Answer

i can combine. thats how my teacher put it in her example

accessdenied · Answer

you could have a lot of different ways to write this, like -1/4 (sqrt(2) + sqrt(6)) or -(sqrt(2) + sqrt(6))/4 wolfram also says this is correct also: http://www.wolframalpha.com/input/?i=sin%283pi%2F4+%2B+5pi%2F6%29+%3D+-1%2F4+%28sqrt%286%29+%2B+sqrt%282%29%29

anonymous · Answer

ill just go with this and if she marks it wrong then ill have to talk to her about it. Thanks for the help!

accessdenied · Answer

Right.  No problem!
I still think if you calculated both out and didn't get the same answer, there was probably just some case of mismatched parentheses or something.  Easily missed!  But best of luck nonetheless!  :)