anonymous
  • anonymous
find the exact value of tan22.5 using the half angle formula. im at ((sqrt2)/(2))/((1+(sqrt2))/(2))
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
thats alot of (((())))) to keep track of :)
anonymous
  • anonymous
sorry!
amistre64
  • amistre64
sqrt(2)/2 ----------- 1+sqrt(2)/2 is what youve got so far?

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anonymous
  • anonymous
yesss
amistre64
  • amistre64
we can "cross out" the /2 parts since 1/2 over 1/2 = 1 sqrt(2) -------- 1+sqrt(2)
amistre64
  • amistre64
now to rationalize the bottom we need to divide by 1-sqrt(2) over 1-sqrt(2)
anonymous
  • anonymous
the conjugate? right?
amistre64
  • amistre64
thats correct, the conjugate...
amistre64
  • amistre64
thats correct, the conjugate...
anonymous
  • anonymous
sorry how do you know when you can multiply by that? is it because i have a + in between the two values on the bottom?
amistre64
  • amistre64
that right, when we have the denominator stuck together by addintion/subtraction, we need to use the conjugate.
anonymous
  • anonymous
and id for example i had 1 - sqrt(2) then i'd still use the opposite sign?
amistre64
  • amistre64
there are 3 things that can happen here: we can multiply by the same value and get: (a+b)(a+b) = (a^2 +2ab +b^2) which doesnt help us out. (a-b)(a-b) = (a^2 -2ab +b^2) which is a bother as well but, (a+b)(a-b) = (a^2 - b^2) which is what will do it for us, so the conjugate is the same first and last, but a change in sign.. make sense?
anonymous
  • anonymous
ahhh i remember now! foiling. sorry im a junior in college taking precal and it's been three years since i saw any algebra so im extremely rusty. it's starting to come back
amistre64
  • amistre64
it was 20 years before I tried college :)
anonymous
  • anonymous
okay so now i used the conjugate and got sqrt(2)-2
amistre64
  • amistre64
thats your top part of the fraction i think sqrt(2) times 1-sqrt(2) = sqrt(2) - 2 the bottom becomes: 1+sqrt(2) times 1- sqrt(2) 1 - 2 = -1 together we get: sqrt(2) - 2 -------- -1 so we have a negative in this thing that needs to be dealt with
amistre64
  • amistre64
pretty much its: -(sqrt(2)-2) = -sqrt(2)+2 = 2-sqrt(2) right?
anonymous
  • anonymous
right

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