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Babynini

  • one year ago

5cos2(theta)=2 Find all solutions in interval [0,2pi)

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  1. Babynini
    • one year ago
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    so cos2(theta)=2/5 2(theta)= ?

  2. Babynini
    • one year ago
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    @peachpi it's a little different.. :P

  3. anonymous
    • one year ago
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    Is that cos 2Θ or cos² Θ?

  4. Babynini
    • one year ago
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    the first

  5. anonymous
    • one year ago
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    ok. so the first thing I like to do when Θ is multiplied is "fix" the interval. 0 ≤ x < 2π Since the x is multiplied by 2, multiply the whole interval by 2 to get 0 ≤ 2x < 4π

  6. anonymous
    • one year ago
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    so we do the same thing we did last time, except now we're looking for solutions from 0 to 4pi. cos 2Θ = 2/5 2Θ = arccos (2/5)

  7. Babynini
    • one year ago
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    arccos(2/5) = 1.159 so we want to add pi to this?

  8. Babynini
    • one year ago
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    or, sorry, subtract this from 2pi

  9. anonymous
    • one year ago
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    You want to divide that by 2 Θ = ½ arccos (2/5) → answer in 1st quadrant on the interval from 0 to 2pi Then add 2pi to get the 1st quad angle between 2pi and 4pi

  10. Babynini
    • one year ago
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    em so the original answer is 0.579 adding 2pi = 6.862

  11. anonymous
    • one year ago
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    the 0.579 is right. and you actually subtract it from 2pi to get the other answer

  12. anonymous
    • one year ago
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    so 5.7

  13. Babynini
    • one year ago
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    *5.8 :)

  14. anonymous
    • one year ago
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    Yes. 5.8 :) There are going to be two more solutions. You got 2Θ = 1.159. Add 2pi to that, then divide by 2 to get the corresponding Θ.

  15. anonymous
    • one year ago
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    should get 3.72

  16. Babynini
    • one year ago
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    Yep yep

  17. anonymous
    • one year ago
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    and then (2pi - 1.159)/2 for the 4th solution is 2.56

  18. Babynini
    • one year ago
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    K so it's theta = 1.159/2 = 0.579 So our first answer: 5.8 add 2pi to that: 3.72 next we have 2pi-0.58 = 5.70 (our third answer) then 5.70 - pi = 2.56 (our fourth answer) haha sorry that's all jumbled up.

  19. Babynini
    • one year ago
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    = 0.58, 3.72,5.70,2.56

  20. anonymous
    • one year ago
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    yep

  21. Babynini
    • one year ago
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    I'll get this. Sometime. thanks!

  22. anonymous
    • one year ago
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    you're welcome

  23. Babynini
    • one year ago
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    @peachpi I just did one by myself!! and got the right answer! xD :')

  24. anonymous
    • one year ago
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    awesome!

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