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anonymous

  • 5 years ago

Find the exact value of sin22.5 (using the half angle formula) i have the answer from the book, but i don't understand how they got there

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  1. amistre64
    • 5 years ago
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    half angle formula is obtained by manipulating the cos(2a) formula

  2. amistre64
    • 5 years ago
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    cos(2a) has 3 equal solutions: cos^2 - sin^2 1 - 2sin^2 2cos^2 -1

  3. amistre64
    • 5 years ago
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    cos(2a) = 1-2sin^2 is helpful in this case.. cos(2a) -1 = 2sin^2 cos(2a) -1 -------- = sin^2 2

  4. anonymous
    • 5 years ago
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    yes, i just don't understand how they simplified this: sqrt ((1 - [sqrt2]/2) / 2) it is supposed to become sqrt ((2 - sqrt2) / 4 )

  5. anonymous
    • 5 years ago
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    they had steps, and it didn't explain how they got from step to step

  6. amistre64
    • 5 years ago
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    ohhhh......

  7. amistre64
    • 5 years ago
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    so you wanna see it simplified then right?

  8. anonymous
    • 5 years ago
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    it just said "common denominator" and i couldn't figure out how to simplify it

  9. anonymous
    • 5 years ago
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    i guess yes, i just want it explained really

  10. amistre64
    • 5 years ago
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    sqrt(1 - cos(45) /2) = sin(22.5) right? sqrt([1 - sqrt(2)/2]/2) we can seperate the "square root" sign to cover the top and bottom of the fraction seperately... for example: sqrt(a/b) = sqrt(a) / sqrt(b) right?

  11. amistre64
    • 5 years ago
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    let me write it out this way so I dont confuse meself: sqrt(2) 1 - ----- 2 ----------- 2

  12. amistre64
    • 5 years ago
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    2 sqrt(2) -- - ------- 2 2 ------------- 2

  13. amistre64
    • 5 years ago
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    2 - sqrt(2) --------- 2 ------------ 2

  14. amistre64
    • 5 years ago
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    2-sqrt(2) 1 -------- x --- 2 2

  15. amistre64
    • 5 years ago
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    2 - sqrt(2) --------- 4 Do you follow that?

  16. anonymous
    • 5 years ago
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    hold on

  17. anonymous
    • 5 years ago
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    i'm confused. i thought you multiplied 2-sqrt(2) 2 -------- x --- 2 1 because 2 is the reciprocal isnt it?

  18. anonymous
    • 5 years ago
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    or am i completely wrong

  19. amistre64
    • 5 years ago
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    lets take a look at a simpler example: 1/2 --- = 1/4 right? 2

  20. amistre64
    • 5 years ago
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    whenever we divide by a fraction we turn it over an multiply instead. 1/2 --- = 1/2 * 1/2 = 1/4 2 1/3 --- = 1/3 * 1/2 = 1/6 2

  21. amistre64
    • 5 years ago
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    7 --- = 7 * (3/1) = 21 1/3

  22. anonymous
    • 5 years ago
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    ohhhhhh got it thnks!

  23. amistre64
    • 5 years ago
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    I knew you would :)

  24. anonymous
    • 5 years ago
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    thank you!

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