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anonymous
 one year ago
Will Medal!
If 2tanx/ (1tan^2x) = 1, then x can equal ____.
Check all that apply.
A) x=5pi/8 + npi
B) x=pi/8 + npi
C) x=3pi/8 + npi
D) x=7pi/8 + npi
anonymous
 one year ago
Will Medal! If 2tanx/ (1tan^2x) = 1, then x can equal ____. Check all that apply. A) x=5pi/8 + npi B) x=pi/8 + npi C) x=3pi/8 + npi D) x=7pi/8 + npi

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I think it is A and B. But this is me taking a guess. I am terrible at trig. Sorry

welshfella
 one year ago
Best ResponseYou've already chosen the best response.3well first cross multiply to give 2 tanx = 1  tan^2 x now rearrange this quadratic: tan^2 x + 2tanx  1 = 0 can you factor this?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes. I am thinking you factor to get tan^2x = 2tan(x)+1?

welshfella
 one year ago
Best ResponseYou've already chosen the best response.3no factor as you would any quadratic like x^2 + 3x + 2 = (x + 1)(x + 2)

welshfella
 one year ago
Best ResponseYou've already chosen the best response.3oh sorry  on second look this will not factor so you need to use the quadratic formula

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So would a = tan^2x b =2tanx and c=1?

welshfella
 one year ago
Best ResponseYou've already chosen the best response.3no a , b and c are the coefficients of tan^2x and tan x so a = 1 , b = 2 and c = 1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So x = +/ sqrt (2) in the end right?

welshfella
 one year ago
Best ResponseYou've already chosen the best response.32 +/ sqrt(4  4*1*1) / 2 = 2 +/ sqrt8 / 2 = (2 +/ 2 * sqrt2 )/ 2 = 1 +/ sqrt2 yep

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Awesome! So now do I just plug in this to my original equation?

welshfella
 one year ago
Best ResponseYou've already chosen the best response.3well they have the answer options in terms of pi so convert everything to decimals so for example 1 + sqrt2 = 0.4142 so find the angle in radians which is the tangent of 0.4142 and see if one of the options gives the the same angle

welshfella
 one year ago
Best ResponseYou've already chosen the best response.3eg angle with tangent 0.4142 = 0.39269 radians now check if pi/8 gives the same value

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So I'm assuming that is one

welshfella
 one year ago
Best ResponseYou've already chosen the best response.3ok so thats one result pi/8 + npi

welshfella
 one year ago
Best ResponseYou've already chosen the best response.3now try the other value for tan x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.01  sqrt 2 = 2.4142 degrees right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok so then the radians of 2.4142 is 0.042135

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't think I did it right

welshfella
 one year ago
Best ResponseYou've already chosen the best response.3no the 2.4142 is the value of tan x so you need tan1(2.4242)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh ok that would make it 1.1781 which is basically the same as 3pi/8 right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So the answers would be pi/8 + npi and 3pi/8 + npi

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Great!! Thank you for taking the time to help me! I feel I really understand now! Thank you!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Weird... I hit the sumit button and it told me it was 5pi/8 instead of 3/pi/8

welshfella
 one year ago
Best ResponseYou've already chosen the best response.3lets check that out

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{2tanx}{1\tan^2x} = 1 \\ \tan(2x)=1\]

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1\[\tan(u)=1 \text{ when } u=?\]

welshfella
 one year ago
Best ResponseYou've already chosen the best response.3ahh i forgot that identity !

welshfella
 one year ago
Best ResponseYou've already chosen the best response.3u = pi/4 of course and x will be pi/8

welshfella
 one year ago
Best ResponseYou've already chosen the best response.3much easier that way lol!

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1and there is also the u=5pi/4 so yep x=5pi/8

welshfella
 one year ago
Best ResponseYou've already chosen the best response.31.1781 is an incorrect result then?  an extraneous result right?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1does give tan(2x) approx 1 what number are you approximating ?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1oh 3pi/8 is what you are approximating

welshfella
 one year ago
Best ResponseYou've already chosen the best response.3sorry I dont follow you yes

welshfella
 one year ago
Best ResponseYou've already chosen the best response.3and 3pi/8 is equivalent to 5pi/8

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1is that not included in the solution: \[\frac{5\pi}{8}+n \pi \\ \text{ if } n=1 \text{ then } \frac{5\pi}{8}\pi=\frac{3\pi}{8}\] so I'm not sure why you say it is extraneous

welshfella
 one year ago
Best ResponseYou've already chosen the best response.3no  i was wrong its not extraneous

welshfella
 one year ago
Best ResponseYou've already chosen the best response.3still i think lehmad learned something along the line...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes I learned a lot! Thank you guys for the help.
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