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    Could someone help me with this please!

    Solve:
    3SinƟ + TanƟ= 0

    Thank you!
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    (Original post by Annabel_lear)
    Could someone help me with this please!

    Solve:
    3SinƟ + TanƟ= 0

    Thank you!


    \tan \theta = \dfrac{\sin \theta}{\cos \theta}


    Multiply through by the denominator.
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    (Original post by Indeterminate)
    \tan \theta = \dfrac{\sin \theta}{\cos \theta}


    Multiply through by the denominator.
    So would that be:
    3sin(theta) + \dfrac{\sin \theta}{\cos \theta} = 0


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    (Original post by Annabel_lear)
    So would that be:
    3sin(theta) + \dfrac{\sin \theta}{\cos \theta} = 0


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    As your first step, yes
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    (Original post by TenOfThem)
    As your first step, yes
    And then multiply by
     cos\theta 

So its: 

3sin\theta cos\theta + sin\theta= 0



Would that turn to 4sin/theta?



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    (Original post by Annabel_lear)
    And then multiply by
     cos\theta 

So its: 

3sin\theta cos\theta + sin\theta= 0
    Yes

    

Would that turn to 4sin/theta?
    No
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    (Original post by TenOfThem)
    Yes



    No
    Oh.. What would you do from there?


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    (Original post by Annabel_lear)
    And then multiply by
     cos\theta 

So its: 

3sin\theta cos\theta + sin\theta= 0



Would that turn to 4sin/theta?



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    factorize it
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    0, pi, arccos(-1/3) these are the solutions in [0,2pi]
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    (Original post by ztibor)
    factorize it
    this
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    Sin theta (3 cos theta + 1 ) = 0

    Now find solutions for Sin theta = 0

    and 3 Cos theta = 0
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    (Original post by charly2012)
    Sin theta (3 cos theta + 1 ) = 0

    Now find solutions for Sin theta = 0

    and 3 Cos theta = 0
    To find solutions would you divide to the otherside? But wouldn't that just make 0?


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    (Original post by Annabel_lear)
    To find solutions would you divide to the otherside? But wouldn't that just make 0?


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    Your solutions would be found within the equations:

    \sin{\theta} = 0 and 3\cos{\theta} + 1 = 0
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    (Original post by Annabel_lear)
    And then multiply by
     cos\theta 

So its: 

3sin\theta cos\theta + sin\theta= 0



Would that turn to 4sin/theta?



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    OK so you've got to this point:
    3sin\theta cos\theta + sin\theta= 0

    Note that both terms on the LHS have a common factor sin\theta so you can factorize it like this:

    sin\theta(3cos\theta + 1) = 0

    Now remember that if you multiply two things together and get zero, one of the things must be zero (or possibly both in some situations!).

    So you can say that EITHER
    sin\theta = 0
    OR
    3cos\theta + 1 = 0

    so you need to find solutions to each of these equations and then combine them to get a complete set of solutions to your original problem
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    (Original post by ztibor)
    factorize it
    Factorise with an 's'
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    (Original post by davros)
    OK so you've got to this point:
    3sin\theta cos\theta + sin\theta= 0

    Note that both terms on the LHS have a common factor sin\theta so you can factorize it like this:

    sin\theta(3cos\theta + 1) = 0

    Now remember that if you multiply two things together and get zero, one of the things must be zero (or possibly both in some situations!).

    So you can say that EITHER
    sin\theta = 0
    OR
    3cos\theta + 1 = 0

    so you need to find solutions to each of these equations and then combine them to get a complete set of solutions to your original problem
    Thank you! Great help


    Posted from TSR Mobile
 
 
 
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