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Math Help - functions

  1. #1
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    functions

    Show graphically or otherwise, that
    sin(x) = m(x)
    has no non-zero solutions for -Pi< x < Pi when m<0

    How would i do this?
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  2. #2
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    I must not be understanding the question correctly.

    Let m(x) = the constant function -1/2. Then m<0 for all x, and sin(x)=m(x) has the solutions x=-\frac{\pi}{6}\text{ and }x=-\frac{5\pi}{6}.

    Do you mean sin(x)=mx? If so, then for x<0, sin(x)<0<mx and for x>0, mx<0<sin(x), so you have your result.

    If you post again to this thread, I'll answer as soon as I can.

    - Hollywood
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  3. #3
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    Quote Originally Posted by hollywood View Post
    I must not be understanding the question correctly.

    Let m(x) = the constant function -1/2. Then m<0 for all x, and sin(x)=m(x) has the solutions x=-\frac{\pi}{6}\text{ and }x=-\frac{5\pi}{6}.

    Do you mean sin(x)=mx? If so, then for x<0, sin(x)<0<mx and for x>0, mx<0<sin(x), so you have your result.

    If you post again to this thread, I'll answer as soon as I can.

    - Hollywood
    yea i meant sin(x) = mx sorry.. how would i do the question graphically?
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  4. #4
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    If you look at the graph of y=sin(x), it has "lobes" in the upper right and lower left quadrants. If m is negative, then y=mx is a line through the origin and is in the upper left and lower right quadrants. So the only place they can meet is at the origin.

    Here's a graph with m=-1.

    Post again in this thread if you're still having trouble.
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