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Math Help - Solving For x (angle)

  1. #1
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    Solving For x (angle)

    #1 Solve: sqrt(3)(cos(x)tan(x) + cos(x) = 0, where 0 <= x <= 2pi
    My work:
    cos(x)[sqrt(3)tan(x) + 1] = 0

    cos(x) = 0
    x = pi/2, 3pi/2

    sqrt(3)tan(x) + 1 = 0
    tan(x) = -1/(sqrt(3)) = opp/adj
    x = 60

    Answer:5pi/6, 11pi/6

    #2 Solve: cos(2x) - 3sin(x) = 2, where -pi <= x <= pi
    1 - (sin(x))^2 - 3sin(x) = 2
    -1 - (sin(x))^2 - 3sin(x) = 0
    Unsure how to continue...

    Answer: 4pi/3, 5pi/3, 3pi/2

    #3 Solve: 2cos(x) = 2^x
    Work: Tried to graph it, but didn't really work out.

    Answer: -1.38, 0 , 0.66
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by AlphaRock View Post

    #2 Solve: cos(2x) - 3sin(x) = 2, where -pi <= x <= pi
    1 - (sin(x))^2 - 3sin(x) = 2
    -1 - (sin(x))^2 - 3sin(x) = 0
    Unsure how to continue...

    Answer: 4pi/3, 5pi/3, 3pi/2


    Answer: -1.38, 0 , 0.66
    \cos{2x}-3\sin{x}=2

    remember

    So, lets' use the third one

    (1-2\sin^2{x})-3\sin{x}=2

    adding

    2\sin^2{x}+3\sin{x}+1=0

    surely you can factor a quadratic expression....
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  3. #3
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    Quote Originally Posted by AlphaRock View Post
    #1 Solve: sqrt(3)(cos(x)tan(x) + cos(x) = 0, where 0 <= x <= 2pi
    My work:
    cos(x)[sqrt(3)tan(x) + 1] = 0

    cos(x) = 0
    x = pi/2, 3pi/2

    sqrt(3)tan(x) + 1 = 0
    tan(x) = -1/(sqrt(3)) = opp/adj
    x = 60

    Answer:5pi/6, 11pi/6

    #2 Solve: cos(2x) - 3sin(x) = 2, where -pi <= x <= pi
    1 - (sin(x))^2 - 3sin(x) = 2
    -1 - (sin(x))^2 - 3sin(x) = 0
    Unsure how to continue...

    Answer: 4pi/3, 5pi/3, 3pi/2

    #3 Solve: 2cos(x) = 2^x
    Work: Tried to graph it, but didn't really work out.

    Answer: -1.38, 0 , 0.66
    Interesting. brentwoodbc asked the same exact questions for #1 and #2 in this thread: http://www.mathhelpforum.com/math-he...functions.html. VonNemo19, don't you remember?


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  4. #4
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    COOL!

    Looks like somebody wants the scholarship too!

    (These are questions from practice exam(s)...)
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  5. #5
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    Can someone show me clearly how to do number 3? And explain why it's a decimal? (I'm used to getting theta where it is radians or degrees (1pi/2 or 90 degrees)
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  6. #6
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    Quote Originally Posted by AlphaRock View Post
    Can someone show me clearly how to do number 3? And explain why it's a decimal? (I'm used to getting theta where it is radians or degrees (1pi/2 or 90 degrees)
    Solutions are in radians.

    x = 0 is an obvious solution easily seen by inspection.

    The other two solutions are decimal approxiations and have been found using technology eg. graphics or CAS calculator. It's not possible to express those answers in exact form.
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  7. #7
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by yeongil View Post
    Interesting. brentwoodbc asked the same exact questions for #1 and #2 in this thread: http://www.mathhelpforum.com/math-he...functions.html. VonNemo19, don't you remember?


    01

    I don't have a memory. My brain is made up of virtual ram. If I shut down my life is over.
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  8. #8
    Senior Member pacman's Avatar
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    # 3 What a weird equation, 2cosx = 2^x. By graphing it, we have four solutions.
    x1 = 0.659958
    x2 = -1.377810
    x3 = -4.321215
    x4 = -7.851817


    Below is the graph of the equation, the red curve is of 2^x and the blue one is of 2cos x. The intersection is the required answer by the proposer.
    Attached Thumbnails Attached Thumbnails Solving For x (angle)-2cosx-2x.gif  
    Last edited by pacman; July 30th 2009 at 03:29 AM. Reason: not clear
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