anonymous
  • anonymous
Find the function value. cos^2(7pi/8)=
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Some sort of half-angle formula applies here.
anonymous
  • anonymous
Ok what should I do?
Psymon
  • Psymon
Mhm, absolutely. Notice that we do not have a common unit circle value for any division of 8. But we do have a value for is 7pi/4. Now in order to actually get the value of 7pi/8, we use a half angle formula. So what we do is we will write out the formula and plug 7pi/4 into that formula, this will give us the value of 7pi/8. So the formula we need to plug 7pi/4 into is this: \[\pm \sqrt{\frac{ 1+\cos2\theta }{ 2 }} \]SO if you plug in 7pi/4 for theta in that formula, you think you could simplify it to find 7pi/8?

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Psymon
  • Psymon
I apologize, looks like only theta, not 2 theta.
anonymous
  • anonymous
\[ \cos^2\left(\frac \theta 2\right) = \frac{1+\cos(\theta)}2 \]
Psymon
  • Psymon
Yeah, once you square it you would have that, lol. I feel bad, still need to correct my mistake in what I posted \[\pm \sqrt{\frac{ 1+\cos \theta }{ 2 }} \]And then yes, wio shortened it by squaring it.
anonymous
  • anonymous
\[ \frac{7\pi}8 = \frac 1 2\left(\frac{7\pi}4\right) \]In this case I would say \(\theta = 7\pi/4\)
anonymous
  • anonymous
so the final answer is 7pi/4? My Math Lab website says it is wrong
anonymous
  • anonymous
No, I'm saying \[ \cos^2\left(\frac{7\pi}8\right)= \frac{1-\cos(7\pi/4)}2 \]Now you have to find \(\cos(7\pi/4)\).
anonymous
  • anonymous
Now we would use: \[ \cos(\theta - 2\pi) = \cos(\theta) \]
anonymous
  • anonymous
so the answer is 1/(square root 2) ?
anonymous
  • anonymous
How did you get that?
anonymous
  • anonymous
cos(7pi/4) = 1/(square root 2)
anonymous
  • anonymous
Okay well if you say that, then we have \[ \frac{1-\frac {1} {\sqrt{2}}}{2} \]And you have to simplify it.
anonymous
  • anonymous
ok
anonymous
  • anonymous
would you show me how to simplify that
anonymous
  • anonymous
It becomes \[ \frac 1 2 - \frac 1 {2\sqrt{2}} \]You want to simplify the radical: \[ \frac 1 2 - \frac {\sqrt{2}} {2} \]Then it is simplified as: \[ \frac {1-\sqrt{2}} 2 \]
anonymous
  • anonymous
hmm for some reason that's wrong idk why
anonymous
  • anonymous
Okay how about \[ \frac {1+\sqrt{2}} 2 \]
anonymous
  • anonymous
are you sure? I only have one attempt left :/
anonymous
  • anonymous
http://www.wolframalpha.com/input/?i=cos^2%287pi%2F8%29
anonymous
  • anonymous
@wio
anonymous
  • anonymous
@cinar how did you use wolfarm alpha to get the answer? it does not show anything related to this
anonymous
  • anonymous
can you send screen shot..
anonymous
  • anonymous
anonymous
  • anonymous
here you go
anonymous
  • anonymous
wolfram says cos^2(7pi/8)=0.8535533905932737622004221810524245196424179688442370... or cos^2(7pi/8)= \[ \frac{1}{4} (2+\sqrt{2}) \]exactly
anonymous
  • anonymous
got it..
anonymous
  • anonymous
cos(2x)=2cos^2x-1 cos^2x=(cos2x+1)/2 x=7pi/8 cos^2(7pi/8)=(cos7pi/4+1)/2 need to find cos(7pi/4) pi=180 degree cos(7pi/4)=cos(7*180/4)=cos(315) cos(315)=cos(360-45)=cos360cos45+sin360sin45=1*1/sqrt2+0*1/sqrt2=1/sqrt2 cos^2(7pi/8)=(cos7pi/4+1)/2=(1/sqrt2+1)/2=\[ \frac{1}{4} (2+\sqrt{2})\]
anonymous
  • anonymous
thank you @cinar yours is right
anonymous
  • anonymous
yw..
anonymous
  • anonymous
@wio thank you too ^^ you made an effort

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