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Math Help - maximum(modified)

  1. #1
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    maximum(modified)

    if xi>0 for 1<=i<=n and
    x1+x2+x3+x4 -------xn=n
    then greatest value of sin x1+sinx2+sinx3+----sin xn=
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  2. #2
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    Quote Originally Posted by ayushdadhwal View Post
    if xi>0 for 1<=i<=n and
    x1+x2+x3+x4 -------xn=n
    then greatest value of sin x1+sinx2+sinx3+----sin xn=
    It looks as though the maximum will occur when x_k = 1 for each k = 1,2,...,n. Then the sum will be n\sin1\approx0.84n. I don't see that it's possible to do any better than that, but I haven't tried to prove it.
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