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    I'm slightly confuses about this question:

    Solve the following for [theta] in the interval 0 < [theta] < (and equal to)360

    tan[theta] = tan[theta](2 + 3sin[theta])

    Is it possible to do:

    tan[theta] / tan[theta] = 2 + 3sin[theta]
    1 = 2 + 3sin[theta]
    sin[theta] = -1/3
    [theta] = -19.5

    This gives me the values of 199.5 and 340.5, but the book also gives the values 180 and 360.

    Why am I missing these values? I don't understand? Could someone kindly explain to me where I'm going wrong?

    Thanks
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    Dividing through by variables can lose you solutions. Instead of cancelling, arrange into a quadratic and factorise.

    Suppose you had x = x(2+3x). Clearly this works if x = 0, but dividing through by x just leaves 1 = 2 + 3x so x = -1/3 (and you miss you out the solution x = 0)
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    Right, I understand tan[theta] = 0 is also a solution (so theta = 180, 360), but I'm not sure how to rearrange to prove this... sorry my mind has just gone blank
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    Move the tan theta on the left to the right:

    0 = tan theta (2 + 3 sin theta) - tan theta

    Expand brackets

    Then factorise.
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    (Original post by mya369)
    Move the tan theta on the left to the right:

    0 = tan theta (2 + 3 sin theta) - tan theta

    Expand brackets

    Then factorise.
    Got it, thanks a lot
 
 
 
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