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anonymous

  • 5 years ago

for what value of on the interval (-9.65, 11.28) will f(x) take on a minimum if f(x)=−7.2sin(0.3x)+1.8cos(0.3x). What is f(x) at this x value? Same question for the maximum on the same interval.

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  1. anonymous
    • 5 years ago
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    this should say for what value of x on the interval... Sorry!

  2. amistre64
    • 5 years ago
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    deriving trig...aint had to do this yet :)

  3. anonymous
    • 5 years ago
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    well the derivative is -0.54sin(0.3x)-2.16(cos(0.3x) if you need it. I know I need to set it to zero to get the critical values, but I don't know how to solve for x lol

  4. amistre64
    • 5 years ago
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    Dx(-7.2 sin(.3x)) = -7.2(.3) cos(.3x)

  5. amistre64
    • 5 years ago
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    lol .... I was getting there :)

  6. anonymous
    • 5 years ago
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    sorry! lol

  7. amistre64
    • 5 years ago
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    lets multiply by 100 to get rid of some of those decimals

  8. amistre64
    • 5 years ago
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    -54 sin(.3x) - 216(cos.3x) = 0

  9. amistre64
    • 5 years ago
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    can we factor out anything from 54 and 216? I know 2 comes out...

  10. anonymous
    • 5 years ago
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    you can take out a 9 i think

  11. amistre64
    • 5 years ago
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    54/216 = 27/108..try 3 now 9/36 try 3 again 3/12 and 3 again 1/4

  12. amistre64
    • 5 years ago
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    looks like 54 factors out completely... 216/54 = anything useful? 4 yay!!

  13. amistre64
    • 5 years ago
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    -54(sin(.3x) + 4cos(.3x)) this look right to you so far?

  14. anonymous
    • 5 years ago
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    yeah I'm following I think. lol, that's what I have when I do the same work on my calculator. :)

  15. amistre64
    • 5 years ago
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    so, lets see what sin(.3x) + cos(.3x) gets us to equal 0

  16. amistre64
    • 5 years ago
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    they gotta be opposites of each other, so lets throw one to the other side

  17. amistre64
    • 5 years ago
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    and dont forget that 4 that I left out lol

  18. anonymous
    • 5 years ago
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    yeah i was going to ask why we weren't using it, lol but nevermind

  19. amistre64
    • 5 years ago
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    4cos(.3x) = - sin(.3x) now picture these graphs for a minute

  20. amistre64
    • 5 years ago
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    the cos is just stretched 4 tall, so the 4 doesnt matter the sin is flipped over upside down

  21. amistre64
    • 5 years ago
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    .3 = the frequency of the graphs

  22. amistre64
    • 5 years ago
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    these cross points at 2 places every time they go thru one frequency...does that make sense?

  23. amistre64
    • 5 years ago
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    once in Q2 and another in Q4

  24. amistre64
    • 5 years ago
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    the only angle that has sin and cos equal is 45 degrees

  25. anonymous
    • 5 years ago
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    right.. I put them in my graphing calculator. lol so that means I have more than one answer right?

  26. amistre64
    • 5 years ago
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    yes... more than one answer, and it will have something to do with 45 degrees

  27. amistre64
    • 5 years ago
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    -9.65 and 11.28 is our interval

  28. amistre64
    • 5 years ago
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    .3(sqrt(2)/2) = ?

  29. anonymous
    • 5 years ago
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    .2121320344

  30. amistre64
    • 5 years ago
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    I might be wrong about the 45 tho :)

  31. amistre64
    • 5 years ago
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    derive it again to see if we can get some useful information...

  32. anonymous
    • 5 years ago
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    derive the original f(x) or take the second derivative?

  33. amistre64
    • 5 years ago
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    second derivative will give us a better picture....

  34. anonymous
    • 5 years ago
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    64.8 sin(0.3 x)-16.2 cos(0.3 x)

  35. amistre64
    • 5 years ago
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    I got: y'' = .648 sin(.3x) - .162 cos(.3x)

  36. anonymous
    • 5 years ago
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    oh, yeah I just had it multiplied by 100 still

  37. amistre64
    • 5 years ago
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    it might be helpful, but im still "stuck" :)

  38. anonymous
    • 5 years ago
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    When I asked a friend, she told me I needed to use the quadratic. However, she had her math major friend do the problem for her, and can't tell me anything farther than that lol

  39. amistre64
    • 5 years ago
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    lets go back to the original.. sin(.3x) + 4cos(.3x)

  40. anonymous
    • 5 years ago
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    Is there a way for us to write them both in the same terms, like a way for us to make cos to sin?

  41. amistre64
    • 5 years ago
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    there can be a square root involved, or a phase shift....

  42. amistre64
    • 5 years ago
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    sin = sqrt(1-cos^2)

  43. amistre64
    • 5 years ago
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    sin^2 = 1-cos^2

  44. anonymous
    • 5 years ago
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    If it helps, when I tried using wolfram alpha, it gives me the answer.. x = 20/3 (pi n+tan^(-1)(1/4 (1+sqrt(17))))

  45. amistre64
    • 5 years ago
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    oww...my eyes.....

  46. anonymous
    • 5 years ago
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    But I don't actually even know what that means, lol so I that wasn't very helpful either. It was kind of a a last resort as it was, because my assignment is due at midnight. :\ lol

  47. amistre64
    • 5 years ago
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    4cos(.3x) = -sin(.3x) square both sides to get 16cos^2(.3x) = sin^2(.3x) 16cos^2(.3x) = 1 - cos^2(.3x)

  48. amistre64
    • 5 years ago
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    then: 17cos^2(.3x) -1 = 0 right?

  49. anonymous
    • 5 years ago
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    i believe you're correct.

  50. amistre64
    • 5 years ago
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    cos^2(.3x) = 1/17

  51. amistre64
    • 5 years ago
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    cos(.3x) = sqrt(17)/17 then ....if that helps :)

  52. anonymous
    • 5 years ago
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    okay so x ends up being like 4.419392212

  53. amistre64
    • 5 years ago
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    cos-1(sqrt(17)/17) is?

  54. anonymous
    • 5 years ago
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    cos-1(sqrt(17)/17) is 1.325817664 i think

  55. amistre64
    • 5 years ago
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    25.32 is what I get for that x :) does that make any sense?

  56. amistre64
    • 5 years ago
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    25.32 radians of course

  57. anonymous
    • 5 years ago
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    ohh.. so why am I getting a different number, is my calculator just in the wrong mode?

  58. amistre64
    • 5 years ago
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    maybe; and I used 1/sqrt(17) to be simple

  59. amistre64
    • 5 years ago
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    lets plug that in to see what we get: sin(.3(25.32)) + 4cos(.3(25.32)) :=: 0 ??

  60. anonymous
    • 5 years ago
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    I'm not getting zero. :\

  61. amistre64
    • 5 years ago
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    0.1321 + 3.9648 = .... ack!!! lol.

  62. amistre64
    • 5 years ago
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    need someone smarter than me I guess :)

  63. anonymous
    • 5 years ago
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    oh no. lol what do I do now? Do you have any ideas of where else I can get help b y midnight?

  64. amistre64
    • 5 years ago
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    how many points it take off if it is wrong?

  65. anonymous
    • 5 years ago
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    I'm not sure.. there are only 4 sections and this one is technically two parts.

  66. amistre64
    • 5 years ago
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    let me review our stuff for a few minutes and see what I can deduce...

  67. anonymous
    • 5 years ago
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    alright. If it helps, on the thread for the problem, it says to take the derivative equal to zero, and that you should get tan=#, then take the inverse.

  68. anonymous
    • 5 years ago
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    I don't know how they're getting tangent though.

  69. anonymous
    • 5 years ago
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    What if we divided both sides by cos(0.3x) and then had tan(0.3x)=4.. does that work?

  70. amistre64
    • 5 years ago
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    -4x -y=0...-y=4x....-y/x = 4 -4x +y = =..... y=4x......y/x=4 this is the tan they get at.... -sin(.3x) ------- = 4 cos(.3x) -sin(x) = sin(-x) so thats the same

  71. amistre64
    • 5 years ago
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    tan(a) = 4 tan-1(4) = what?

  72. amistre64
    • 5 years ago
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    i was getting to it.... :)

  73. amistre64
    • 5 years ago
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    75.96 degrees is a divide that by.3

  74. anonymous
    • 5 years ago
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    so we have 253.212=x ?

  75. anonymous
    • 5 years ago
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    that sounds large. lol

  76. amistre64
    • 5 years ago
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    remember that tan-1 spits out an angle between -90 and 90

  77. amistre64
    • 5 years ago
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    (75.96 + 180) /.3 ?? maybe

  78. amistre64
    • 5 years ago
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    (75.96 - 90)/.3?

  79. anonymous
    • 5 years ago
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    that one gives us -46.8

  80. amistre64
    • 5 years ago
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    i see that..... maybe our interval itself gives us a max or min at the end points?

  81. anonymous
    • 5 years ago
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    if you put those in.. for -9.65, we get 0.0119783705 and for 11.28, we get -0.190832377

  82. amistre64
    • 5 years ago
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    .3x gives us one cycle every 20pi/3 does that helps us out?

  83. anonymous
    • 5 years ago
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    well in the wolfram alpha, it said something about 20/3 pi * n, but n is supposed to mean any integer, so I didn't really understand it.

  84. amistre64
    • 5 years ago
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    n = the angle measurement a normal cycle is 2pi but we disturb that with .3.... so it increases the frequency of the cycle to 20pi/3

  85. amistre64
    • 5 years ago
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    6 and 2/3 pi

  86. anonymous
    • 5 years ago
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    x = 20/3 (pi n+tan-1(1/4 (1+sqrt(17))))

  87. amistre64
    • 5 years ago
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    What is the value of our interval in terms of pi?

  88. amistre64
    • 5 years ago
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    x(pi) = -9.65 x = pi/-9.65

  89. amistre64
    • 5 years ago
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    -.325 pi to .279 pi right?

  90. amistre64
    • 5 years ago
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    that aint gonna make a difference, becasue our interval is telling us the value of "x" which is the angle involved.... not the period....

  91. anonymous
    • 5 years ago
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    okay.. I'm just lost at this point. lol I really don't even know how to get any further in this.

  92. amistre64
    • 5 years ago
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    im at a loss for the moment as well :) its all those decimals that are messing me up

  93. anonymous
    • 5 years ago
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    I've got it!!!! lol I graphed it and just followed the graph and put in the numbers :P thanks though hahah

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