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Math Help - Trig General Solutions

  1. #1
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    Exclamation Trig General Solutions

    Hi

    For tan x = sin x, why is the general solution only x = pi*n and not also x=2pi*n?

    Similarly, for cos (3x) = cos (x), why is it only x = pi*n/2 and not also x = pi*n?

    Thanx!
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  2. #2
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    Quote Originally Posted by xwrathbringerx View Post
    Hi

    For tan x = sin x, why is the general solution only x = pi*n and not also x=2pi*n?

    Similarly, for cos (3x) = cos (x), why is it only x = pi*n/2 and not also x = pi*n?

    Thanx!
    In both cases the second solution you state is a subset of the first eg. x = 2 \pi n is a subset of x = \pi n where n is an integer.

    Write out some of the concrete solutions that both expressions give and you will see this.
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  3. #3
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    Hey is it alrite to write both as solutions i.e. x = .... or ..... OR do i hav to just write the 1st solution?
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  4. #4
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    Quote Originally Posted by xwrathbringerx View Post
    Hey is it alrite to write both as solutions i.e. x = .... or ..... OR do i hav to just write the 1st solution?
    Well, writing both is not wrong so I doubt you'd be penalised in an exam. But if you can recognise that one general solution is a subset of another, you'll have a more elegant answer.

    But if in the slightest doubt, you should always write both.
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