anonymous
  • anonymous
Find an exact value. sine of nineteen pi divided by twelve. quantity square root of two minus square root of six divided by four. quantity square root of six minus square root of two divided by four. quantity square root of six plus square root of two divided by four. quantity negative square root of six minus square root of two divided by four. @ganeshie8
Mathematics
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anonymous
  • anonymous
Find an exact value. sine of nineteen pi divided by twelve. quantity square root of two minus square root of six divided by four. quantity square root of six minus square root of two divided by four. quantity square root of six plus square root of two divided by four. quantity negative square root of six minus square root of two divided by four. @ganeshie8
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
anonymous
  • anonymous
zepdrix
  • zepdrix
wut 0_o wuts going on here

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anonymous
  • anonymous
i need help with this
zepdrix
  • zepdrix
\[\Large\rm \sin\left(\frac{19\pi}{12}\right)=\sin\left(\frac{19\pi/6}{2}\right)\]We can start there, ya? And maybe apply half-angle formula? What do you think? :3
anonymous
  • anonymous
okay yes
zepdrix
  • zepdrix
\[\Large\rm \sin\left(\frac{\color{orangered}{\theta}}{2}\right)=\pm\sqrt{\frac{1-\cos\color{orangered}{\theta}}{2}}\]
zepdrix
  • zepdrix
So then for our problem,\[\Large\rm \sin\left(\frac{\color{orangered}{19\pi/6}}{2}\right)=\pm\sqrt{\frac{1-\cos\color{orangered}{\frac{19\pi}{6}}}{2}}\]
anonymous
  • anonymous
ok
zepdrix
  • zepdrix
What's cosine of 19pi/6? Hmm that angle is too large.. it's larger than 2pi, so we should try to unwind it by subtracting some 2pi's from it
zepdrix
  • zepdrix
\[\Large\rm \frac{19\pi}{6}-2\pi\quad=\quad \frac{19\pi}{6}-\frac{12\pi}{6}=\frac{7\pi}{6}\]Ya?
zepdrix
  • zepdrix
So our problem becomes,\[\Large\rm \pm\sqrt{\frac{1-\cos\color{orangered}{\frac{7\pi}{6}}}{2}}\]
zepdrix
  • zepdrix
All we did was spin around the circle once and land in the same spot, to get a better angle to work with.
zepdrix
  • zepdrix
Now simplify +_+
anonymous
  • anonymous
i have trouble simplifying that..
zepdrix
  • zepdrix
bust out your unit circle or something.. to get the cosine value :U requires some memorization to get those down
zepdrix
  • zepdrix
cosine is the x coordinate
anonymous
  • anonymous
\[-\sqrt{6}-\sqrt{2}/4?\]
anonymous
  • anonymous
is that it?
anonymous
  • anonymous

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