something fundamental I seem to be missing

A

allegansveritatem

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Jan 10, 2018
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Here is the problem:43prob1.PNG
Here is the graph alluded to above:43graph.PNG
I am asking about part b) of problem. Here is what I did with it:43partb.PNG
I feel stupid asking this but I can't come up with a method of solution such that I clearly understand why it works. I have a strong sense that I know something here that is hiding from me. I have the answer to this in my solutions manual but the solution is cryptic--as many of them are. Usually this crypticness (?) is OK. I wan work with it. But here it leaves me wondering what the **** went on. So...can anyone suggest what it is I need to know here? I will post the solution in the following post--they only allow three images per post.
 
They tell you that P, Q and R are solutions to sin(2x) + sin(x) = 0, and you found those solutions. Now which of those 5 x-values which you found corresponds to the x-values for P, Q and R?? Now do what The Cat suggested.
 
Jomo said:
They tell you that P, Q and R are solutions to sin(2x) + sin(x) = 0, and you found those solutions. Now which of those 5 x-values which you found corresponds to the x-values for P, Q and R?? Now do what The Cat suggested.
Click to expand...
I see it now. Well, I did say it was something fundamental. At least I got that right. What is it that they say? Ignorance is temporary but dumb is forever. I'm not sure which of these conditions applies to me but I will give myself the benefit of the doubt and go with the former.
 
allegansveritatem said:
What is it that they say? Ignorance is temporary but dumb is forever. I'm not sure which of these conditions applies to me but I will give myself the benefit of the doubt and go with the former.
Click to expand...
Taking that as an exercise in mathematical logic, given the premise, I would conclude that if you have ever learned something, then you are not dumb, because if you were dumb, it would never change. QED
 
QED indeed. Actually I think the best way to deal with others is to assume, no matter how they appear, that they are anything but dumb. Everyone knows astonishingly more than they or anyone else thinks they do.
 
allegansveritatem said:
QED indeed. Actually I think the best way to deal with others is to assume, no matter how they appear, that they are anything but dumb. Everyone knows astonishingly more than they or anyone else thinks they do.
Click to expand...
Depending on how useful their knowledge is........?:cautious:.
 
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