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Math Help - Roots

  1. #1
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    Roots

    ((cosx)^2)(1+3(sinx)^2)=1

    How do I find the root 54.7?
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  2. #2
    Member Mathelogician's Avatar
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    What do you mean by the root 54.7?

    You can use the identity sinx^2+cosx^2=1 to converte sine into cosine or cosine into sine form and then solve the quadratic eqution. Just check your final solutions because of the equation's beeing in quadratic form...
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  3. #3
    Grand Panjandrum
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    Do what Mathelogician says, giving you an equation in [sin(x)]^2, then substitute u=[sin(x)]^2 which gives you a quadratic in $$ u, solve that then ...

    CB
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  4. #4
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    I think I have done it now. I did not get a quadratic equation. I got 2x^2-3x^4=0. I take out the factor 2x^2 and then 1-(3/2)x^2=0 gives the solutions other than 0, 180 and 360.
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  5. #5
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    Is it generally preferable to let u=(sin x)^2 or let u=sin x?
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  6. #6
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    Quote Originally Posted by Stuck Man View Post
    Is it generally preferable to let u=(sin x)^2 or let u=sin x?
    They are equivalent if you are careful about sines, but if the right hand side had been something other than 1 you would have ended up with the equivalent of u=(sin(x))^2 to get a quadratic.
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  7. #7
    Member Mathelogician's Avatar
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    Yes it's not quadratic and may seem a bit complicated.
    Try this:
    To avoid confusion let sinx = a and cosx = b and sin(2x)=c
    so we have b^2+3(ab)^2=1 => 3(ab)^2=1-b^2=a^2 => (3/4)c^2 = a^2 =>
    (3/4)c^2 - a^2 = 0 => (sqrt3/2 c - a)(sqrt3/2 c + a)=0
    Then solve each expression; Just in solving each one, remember that sin(2x)=2sinx.cosx
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