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Math Help - Evaluate trigo expression

  1. #1
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    Evaluate trigo expression

    How to evaluate: Sinx - 2sin4x + sin6x
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  2. #2
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    More information please

    Hello owen8810

    Welcome to Math Help Forum!
    Quote Originally Posted by owen8810 View Post
    How to evaluate: Sinx - 2sin4x + sin6x
    Sorry, I don't understand what is wanted here. Could you give us the original question, please?

    Grandad
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    Quote Originally Posted by Grandad View Post
    Hello owen8810

    Welcome to Math Help Forum!Sorry, I don't understand what is wanted here. Could you give us the original question, please?

    Grandad
    evaluate or simplify: sin4 - 2sin4x + sin6x

    thks.
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  4. #4
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    Trig Formulae

    Hello owen8810
    Quote Originally Posted by owen8810 View Post
    evaluate or simplify: sin4(?) - 2sin4x + sin6x

    thks.
    This doesn't really help, especially as you have a typo in your reply.

    Evaluate and simplify mean two different things: evaluate means 'find the value of', and simplify means 'write in a simpler form'.

    We can only evaluate a function of x if we know a particular value or values of x to substitute into the function. So that still doesn't make sense here.

    The only way you could simplify an expression like this is to use trig formulae to write it in an alternative form, and hope that you can then write the result more simply. I can think of two possibilities here:

    • Use formulae for \sin 4x and \sin 6x in terms of single angles; you'll find the formulae here, for example.
    • Re-write \sin x - 2\sin4x+\sin 6x as (\sin x - \sin 4x) + (\sin 6x - \sin 4x), and then use the formula \sin A - \sin B = 2\cos\tfrac12(A+B)\sin\tfrac12(A-B) for each part of the expression.

    I have tried both of these approaches, and I can't see that the results are any simpler than the original expression! So unless we have some more information, I can't see how we can proceed further.

    Grandad
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