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    Solve for t (theta), giving all roots in the interval 0 =< t =< 360:

    1) 4sin^2 t cos t = tan^2 t.

    Right so I started by doing the following:

    4 - 4cos^2 cos t = sin^2 t / cos^2 t,
    cos^2 t (4 - 4cos^2 cos t) = 1 - cos^2 t,
    cos^2 t (4 - 4cos^3 t) = 1 - cos^2 t,
    4 cos^2 t - 4 cos^5 t = 1 - cos^2 t,
    Then use x = cos t to do:
    4x^2 - 4x^5 = 1 - x^2,
    = 5x^2 - 4x^5 - 1 = 0.

    Is this right? If so, how would I factorise?
    If it is incorrect, what is the correct way to do this?

    Many thanks
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    Not sure if this is the best way either, but I found a more manageable solution.

    Try dividing by the Sin^2(t) in the first equation and see where it takes you.
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    (Original post by Quadratic)
    Not sure if this is the best way either, but I found a more manageable solution.

    Try dividing by the Sin^2(t) in the first equation and see where it takes you.
    Surely that would make it more difficult? And can you divide by sin^2 t in this case? Our teacher says it eliminates a solution or something...
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    (Original post by adil12)
    Surely that would make it more difficult? And can you divide by sin^2 t in this case? Our teacher says it eliminates a solution or something...
    Ah damn yeah, never thought about that. I have a habit of dividing by 0. 2 min.
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    x = 1 is a solution to the equation.
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    (Original post by jaheen22)
    x = 1 is a solution to the equation.
    How did you work it out?
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    (Original post by adil12)
    How did you work it out?
    Just by looking at it:

    5(1)^2 - 4(1)^5 - 1 = 0
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    Anybody know if my method is correct and if so, how to factorise it to find the solutions?
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    4sin^2(t)cos(t) = tan^2(t)
    4sin^2(t)cos(t) = sin^2(t) / cos^2(t)
    4sin^2(t)cos^3(t) = sin^2(t)
    sin^2(t)[4cos^3(t) - 1] = 0

    t = sin^-1(0) OR t = cos^-1((1/4)^(1/3))
    t = ...
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    (Original post by adil12)
    How did you work it out?
    The equation is wrong though I think it should be:

    4x^5 - 4x^3 - x^2 + 1 = 0

    Where x = 1 is still a solution.
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    (Original post by Murrayland)
    4sin^2(t)cos(t) = tan^2(t)
    4sin^2(t)cos(t) = sin^2(t) / cos^2(t)
    4sin^2(t)cos^3(t) = sin^2(t)
    sin^2(t)[4cos^3(t) - 1] = 0

    t = sin^-1(0) OR t = cos^-1((1/4)^(1/3))
    t = ...
    Cheers aha, this was bugging me. Seems I can't do C2 any more :P
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    (Original post by Murrayland)
    4sin^2(t)cos(t) = tan^2(t)
    4sin^2(t)cos(t) = sin^2(t) / cos^2(t)
    4sin^2(t)cos^3(t) = sin^2(t)
    sin^2(t)[4cos^3(t) - 1] = 0

    t = sin^-1(0) OR t = cos^-1((1/4)^(1/3))
    t = ...
    Thanks a lot mate! Repped
 
 
 
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