#math - Thu 10 May 2007 between 02:07 and 02:05

mk_but how do I figure out the distance?
TRWBWmk_: c(t)=c0+t*v, define the line with a unit normal to it, get a quadradic
mk_since there are an infinite number of points on the line
unit normal to it?
TRWBWmk_: define the line as ax+by=c, or {a,b}.{x,y}=c
TRWBWmk_: {a,b} is a normal vector to the line
anubissi have some problems with trig identities
i have to integrate sqrt(1 -sin(t) )
TRWBWmk_: if it's a unit normal, then |{a,b}.{x,y}-c| is distance to the line
Eclipsorsubstitute, anubiss ?
mk_what is the {a,b}.{x,y} notation?
Eclipsorand remember that cos is an evil derivative because it turns sin negative while sin is all peaceful and turns into positive cosine :)
anubissi can use the conjugate to obtain: sqrt( 1 - sin(t) ) * ( ( 1+sin(t) ) / ( ( 1+ sin(t) ) )
TRWBWmk_: i use . for dot
mk_: raise it up half a line height and it looks like dot product
anubissand the answer book gives after this step : sqrt( cos^2(t) / sqrt(1+ sin(t)
and i dont undetstand
droptothetopIn relation to existence and uniqueness of a solution to a differential equation, if it's determined that there is no unique solution given a certain initial condition how can you show that there is more than one solution?
One way would be to solve the equation.
anubissfirst i dont understand how you can multiply 1 - sin(t) by 1+ sin(t) and second the answer cos^2 ..
droptothetopBut how to show that there are two?
TRWBWdroptothetop: how about f+1=f, that's a differential equation with no unique solution
Olatheanubiss: (1 - sin)(1 + sin) = 1 - sin^2. cos^2 + sin^2 = 1.
first i dont understand how you can multiply sqrt(1 - sin(t)) by sqrt(1+ sin(t)).. they are different!
Olatheanubiss: (1 - sin)(1 + sin)/(1 + sin)
droptothetopTRWBW, well, I am speaking specifically about ones that are given initial conditions, and at those initial conditions there is discontinuity in f(y,t) in y'=f(y,t)
anubisshum, well my problem boils down to the sqrt's
Olatheanubiss: a = ab/b
anubisswhy do you remove them
TRWBWdroptothetop: f=1+f, f(0)=1
droptothetopor in d f(y,t) /dy
Olatheanubiss: Where are they removed ?
mk_ok, I see what the dot product is. I use a and b from the line, and x and y from the circle... what's c then?
anubissi see so you dont care about the sqrt's you just multiply whats inside
TRWBWmk_: that lets you shift the line.

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