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Prove that sinx=x for x is a real number has only one solution at x=0

  • math -

    on the same grid, graph both
    y = x, which is a straight line, with slope 1
    y = sinx

    http://www.wolframalpha.com/input/?i=plot+y+%3D+x,+y+%3D+sinx

    What do you notice?
    Where do they intersect ?

    slope of y = sinx
    = dy/dx = cosx

    when x = 0, cos0 = 1
    for any value of -π/2 < x < p/2 , cosx < 1
    so the graphs rise at different rates and will never meet again.

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