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anonymous
 one year ago
Find the exact value
tan(9pi/8) Using half life formula
anonymous
 one year ago
Find the exact value tan(9pi/8) Using half life formula

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Would the 9pi/8 change to 9pi/4?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Hehe, I like how you called it halflife formula :P Well, the idea is that \[\tan(x/2) = \frac{ 1cosx }{ sinx }\] What you want to do is rewrite 9pi/8 as x/2. So if 9pi/8 = x/2, what is x?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh you already answered that, yes, you would use 9pi/4 in the formula, lol.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I meant half angle lol, my formula is different from that one

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\tan \theta/2=\sqrt{1\cos \theta/1+\cos \theta}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It'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) = \[\sqrt{\frac{ 1cosx }{ 1+cosx }}\] \[\frac{ 1cosx }{ sinx }\] or \[\frac{ sinx }{ 1+cosx }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yep. So choose whichever one you like and plug in 9pi/4 :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0But 9pi/4 isnt on my unit circle

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well, 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
 one year ago
Best ResponseYou've already chosen the best response.0is it just simply 7pi/4?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well, 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
 one year ago
Best ResponseYou've already chosen the best response.0I think so yeah, how did you know what 2pi is equivalent to 8pi/4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 2\pi }{ 1 }*\frac{ 4 }{ 4 } = \frac{ 8\pi }{ 4 }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[=\sqrt{1(2/\sqrt2)/1+(2/\sqrt2)}\] Kay, With my formula I have this

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You have the square roots reverse. it should be \(\sqrt{2}/2\) on each of those.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Would I then multiple the 2 to everything?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0To reduce it, yes :3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Should I leave it like it is after that

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That 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
 one year ago
Best ResponseYou've already chosen the best response.0thank you, I have two more problems to do

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thats fine, seems like I have time
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