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?
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 .
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.
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.