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anonymous

  • 5 years ago

find the exact value of tan22.5 using the half angle formula. im at ((sqrt2)/(2))/((1+(sqrt2))/(2))

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  1. amistre64
    • 5 years ago
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    thats alot of (((())))) to keep track of :)

  2. anonymous
    • 5 years ago
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    sorry!

  3. amistre64
    • 5 years ago
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    sqrt(2)/2 ----------- 1+sqrt(2)/2 is what youve got so far?

  4. anonymous
    • 5 years ago
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    yesss

  5. amistre64
    • 5 years ago
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    we can "cross out" the /2 parts since 1/2 over 1/2 = 1 sqrt(2) -------- 1+sqrt(2)

  6. amistre64
    • 5 years ago
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    now to rationalize the bottom we need to divide by 1-sqrt(2) over 1-sqrt(2)

  7. anonymous
    • 5 years ago
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    the conjugate? right?

  8. amistre64
    • 5 years ago
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    thats correct, the conjugate...

  9. amistre64
    • 5 years ago
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    thats correct, the conjugate...

  10. anonymous
    • 5 years ago
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    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?

  11. amistre64
    • 5 years ago
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    that right, when we have the denominator stuck together by addintion/subtraction, we need to use the conjugate.

  12. anonymous
    • 5 years ago
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    and id for example i had 1 - sqrt(2) then i'd still use the opposite sign?

  13. amistre64
    • 5 years ago
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    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?

  14. anonymous
    • 5 years ago
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    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

  15. amistre64
    • 5 years ago
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    it was 20 years before I tried college :)

  16. anonymous
    • 5 years ago
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    okay so now i used the conjugate and got sqrt(2)-2

  17. amistre64
    • 5 years ago
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    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

  18. amistre64
    • 5 years ago
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    pretty much its: -(sqrt(2)-2) = -sqrt(2)+2 = 2-sqrt(2) right?

  19. anonymous
    • 5 years ago
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    right

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