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anonymous

  • 5 years ago

Solve this equation on the interval 0\[\le\] θ < 2π. If there is only one solution, write it in the upper box and write NONE in the lower box. If there is no solution, write NONE in both boxes. Round your answer(s) to two decimal places using radians. θ = (smaller value of θ) θ = (larger value of θ)

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  1. amistre64
    • 5 years ago
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    there is no equation here...

  2. anonymous
    • 5 years ago
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    haha really? why is that?

  3. amistre64
    • 5 years ago
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    Its alot of instructions on what to do; but there is no equation to work it on lol

  4. anonymous
    • 5 years ago
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    lol!! sorry!!

  5. anonymous
    • 5 years ago
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    i got it here

  6. anonymous
    • 5 years ago
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    sintheta + sqrt3costheta = 1

  7. amistre64
    • 5 years ago
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    sin(t) + sqrt(3)cos(t) = 1 right?

  8. anonymous
    • 5 years ago
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    yes

  9. amistre64
    • 5 years ago
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    then.... sqrt(3)cos(t) = 1 - sin(t) 3cos^2 = 1 +sin^2 -2sin... lets cheat and do this lol http://www.wolframalpha.com/input/?i=sin%28t%29+%2B+sqrt%283%29cos%28t%29+%3D+1

  10. anonymous
    • 5 years ago
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    hahaha thats the way!

  11. anonymous
    • 5 years ago
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    damn it im not gettin it!

  12. amistre64
    • 5 years ago
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    i cant seem to get it out either.... i know theres one answer at least; might have to just make a chart and narrow it in

  13. amistre64
    • 5 years ago
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    an alternative form is: \[4\sin[\frac{\pi}{4}-\frac{t}{2}] . \sin[\frac{t}{2}+\frac{\pi}{12}]=0\]

  14. anonymous
    • 5 years ago
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    ohkay...lol

  15. amistre64
    • 5 years ago
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    since sin = 0 at 0 and pi; we can prolly figure out a few t's from this ?

  16. amistre64
    • 5 years ago
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    t/2 = pi/4 t = pi/2sounds reasoneable plug it into the orifinal and test

  17. anonymous
    • 5 years ago
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    i think ur getin somewhere haha

  18. amistre64
    • 5 years ago
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    the other seems to be -pi/6 but that aint in the inteval is it lol

  19. anonymous
    • 5 years ago
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    lol no it isnt haha

  20. amistre64
    • 5 years ago
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    sin(pi / 2) + (sqrt(3) * cos(pi / 2)) = 1 is good tho

  21. anonymous
    • 5 years ago
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    would that be the lower value or upper value?

  22. amistre64
    • 5 years ago
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    thats the lower value

  23. anonymous
    • 5 years ago
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    i only get two shots so i probably beta wait till we figur out the upper value lol

  24. amistre64
    • 5 years ago
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    its close to 2pi according to the graph

  25. amistre64
    • 5 years ago
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    now we know -pi/6 is good; but if we take and try to reach that going from 0 to 2pi what do we get? i wonder

  26. amistre64
    • 5 years ago
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    11pi/6 right?

  27. amistre64
    • 5 years ago
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    sin((11 * pi) / 6) + (sqrt(3) * cos((11 * pi) / 6)) = 1: from google

  28. anonymous
    • 5 years ago
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    howd u get tht?

  29. anonymous
    • 5 years ago
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    11pi/6 from -p1/6 ?

  30. amistre64
    • 5 years ago
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    all angles have many names to them because when you walk around a circle you can go along way and still get nowhere

  31. amistre64
    • 5 years ago
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    we can walk -pi/6 to smell the roses; or we can take the long way around; and walk 11pi/6 to get to the same place to wmell the roses

  32. anonymous
    • 5 years ago
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    lol. so u added two pi?

  33. amistre64
    • 5 years ago
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    I did ;)

  34. anonymous
    • 5 years ago
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    haha. it works doesnt it?

  35. amistre64
    • 5 years ago
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    it does indeed :) becuase they both have the same values

  36. anonymous
    • 5 years ago
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    kay so u reckon i should give pi/2 and 11pi/6 a shot?

  37. amistre64
    • 5 years ago
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    i do..

  38. anonymous
    • 5 years ago
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    yay ur a genius!!! it works haha

  39. amistre64
    • 5 years ago
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    lol .... i had to remember my trigs :)

  40. anonymous
    • 5 years ago
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    haha. is there a simpler way of doing this tho?

  41. amistre64
    • 5 years ago
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    i caouldnt find a way to get it into the alternate form; but wolfram did... so i tested that forms results into the original and they worked like a charm

  42. anonymous
    • 5 years ago
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    good ole wolfram lol

  43. anonymous
    • 5 years ago
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    so are you a teacher?

  44. amistre64
    • 5 years ago
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    no, just old :) im trying to get my masters degree in math tho so I can teach college math

  45. anonymous
    • 5 years ago
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    good effort. you'll get there mate haha

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