anonymous
  • anonymous
Find the exact value tan(9pi/8) Using half life formula
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
Would the 9pi/8 change to 9pi/4?
anonymous
  • anonymous
Hehe, I like how you called it half-life formula :P Well, the idea is that \[\tan(x/2) = \frac{ 1-cosx }{ sinx }\] What you want to do is rewrite 9pi/8 as x/2. So if 9pi/8 = x/2, what is x?
anonymous
  • anonymous
Oh you already answered that, yes, you would use 9pi/4 in the formula, lol.

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anonymous
  • anonymous
I meant half angle lol, my formula is different from that one
anonymous
  • anonymous
\[\tan \theta/2=\sqrt{1-\cos \theta/1+\cos \theta}\]
anonymous
  • anonymous
It's an equivalent formula. There are 3 formulas you can usefor tan(x/2), i just chose one of the simple ones. These are the 3 you can use: tan(x/2) = \[\sqrt{\frac{ 1-cosx }{ 1+cosx }}\] \[\frac{ 1-cosx }{ sinx }\] or \[\frac{ sinx }{ 1+cosx }\]
anonymous
  • anonymous
Oh okay
anonymous
  • anonymous
Yep. So choose whichever one you like and plug in 9pi/4 :)
anonymous
  • anonymous
But 9pi/4 isnt on my unit circle
anonymous
  • anonymous
Well, any value on the unit circle is equivalent to adding or subtracting multiples of 2pi. So what we can do is subtract 2pi from 9pi/4 to get an equivalent angle that wil be on the unit circle.
anonymous
  • anonymous
is it just simply 7pi/4?
anonymous
  • anonymous
Well, 2pi is equivalent to 8pi/4. Subtracting that for 9pi/4, we would have 9pi/4 - 8pi/4 = pi/4. Does that make sense?
anonymous
  • anonymous
I think so yeah, how did you know what 2pi is equivalent to 8pi/4
anonymous
  • anonymous
\[\frac{ 2\pi }{ 1 }*\frac{ 4 }{ 4 } = \frac{ 8\pi }{ 4 }\]
anonymous
  • anonymous
\[=\sqrt{1-(2/\sqrt2)/1+(2/\sqrt2)}\] Kay, With my formula I have this
anonymous
  • anonymous
You have the square roots reverse. it should be \(\sqrt{2}/2\) on each of those.
anonymous
  • anonymous
Oh right
anonymous
  • anonymous
Would I then multiple the 2 to everything?
anonymous
  • anonymous
To reduce it, yes :3
anonymous
  • anonymous
Should I leave it like it is after that
anonymous
  • anonymous
That would be up to your professor. You would have: \[\sqrt{\frac{ 2-\sqrt{2} }{ 2+\sqrt{2} }}\] Now, because of the formula I mentioned, this is equivalent to: \[\frac{ \sqrt{2} }{ 2+\sqrt{2} }\] which could be rationalized. So considering the two are equal, it really is up to the professor on how much crazy simplification you have to do.
anonymous
  • anonymous
thank you, I have two more problems to do
anonymous
  • anonymous
Thats fine, seems like I have time

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