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anonymous

  • one year ago

Solve: 1-sin(2πt)=0, for 0≤t≤2.

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  1. Michele_Laino
    • one year ago
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    we have: \[\Large \sin \left( {2\pi t} \right) = 1\]

  2. Michele_Laino
    • one year ago
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    now: sin x= 1 when: \[x = \frac{\pi }{2},2\pi + \frac{\pi }{2},4\pi + \frac{\pi }{2}...\]

  3. Michele_Laino
    • one year ago
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    for example, for the first solution, pi/2, we can write: \[2\pi t = \frac{\pi }{2}\] please solve for t

  4. anonymous
    • one year ago
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    t=2π?

  5. triciaal
    • one year ago
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    no try again

  6. anonymous
    • one year ago
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    t=π^2?

  7. triciaal
    • one year ago
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    |dw:1437338469566:dw|

  8. triciaal
    • one year ago
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    |dw:1437338527982:dw|

  9. triciaal
    • one year ago
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    need the words?

  10. triciaal
    • one year ago
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    are you here?

  11. anonymous
    • one year ago
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    Oh... lol I am an idiot. xD

  12. Nnesha
    • one year ago
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    nah u r no8 :=)

  13. anonymous
    • one year ago
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    Wait, so is 1/4 the answer?

  14. zepdrix
    • one year ago
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    \[\large\rm 2\pi t=\frac{\pi}{2}+2\pi k,\qquad k\in \mathbb{Z}\]Dividing by 2pi,\[\large\rm t=\frac{1}{4}+k,\qquad k\in \mathbb Z\]When k=0, yes you get t=1/4. That is one of your solutions. Think of other integers though. Which other integers for k will keep our t between 0 and 2?

  15. anonymous
    • one year ago
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    Um... 3pie over 2?

  16. freckles
    • one year ago
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    integers. 3pi/2 is not an integer t=1/4+k where k is an integer are your candidates for solutions in the interval [0,2] notice for k=0 you have t=1/4 what happens if you let k=1?

  17. anonymous
    • one year ago
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    So... 0 and 2?

  18. freckles
    • one year ago
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    so we want to find t in [0,2] such that \[0 \le t \le 2 \\ 0 \le \frac{1}{4}+k \le 2 \text{ from here you decide what \to \choose for } k \\ 0-\frac{1}{4} \le k \le 2-\frac{1}{4} \\ \text{ I subtracted } \frac{1}{4} \text{ on both sides } \\ \frac{-1}{4} \le k \le \frac{7}{4}\] what are the only integers in that inequality ?

  19. anonymous
    • one year ago
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    0 and 2?

  20. freckles
    • one year ago
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    do you mean 0 and 1?

  21. freckles
    • one year ago
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    7/4 is less than 2 so 2 can't be included in that inequality above

  22. anonymous
    • one year ago
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    Oh i see.

  23. freckles
    • one year ago
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    |dw:1437428007076:dw| only integers between -1/4 and 7/4 is 0 and 1

  24. freckles
    • one year ago
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    so these are the integers that @zepdrix was referring to

  25. freckles
    • one year ago
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    he already entered in 0 for k to get one solution for t now you just have to enter in 1 for k to get the other solution for t

  26. freckles
    • one year ago
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    \[t=\frac{1}{4}+k \\ \text{ when } k=0 \text{ we have } t=\frac{1}{4}+0=\frac{1}{4} \\ \text{ when } k=1 \text{ we have } t=?\]

  27. freckles
    • one year ago
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    I'm just asking you to replace k with 1

  28. freckles
    • one year ago
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    t=1/4+1=?

  29. anonymous
    • one year ago
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    5/4

  30. freckles
    • one year ago
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    yes t=1/4 or t=5/4 are the only solutions for t in the given interval

  31. anonymous
    • one year ago
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    Wow. that was intense... lol

  32. anonymous
    • one year ago
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    Thank you

  33. freckles
    • one year ago
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    np lol the word intense is intense by itself (to me anyways)

  34. anonymous
    • one year ago
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    Haha. Yea it is huh? xD

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