Would anyone mind going over the basic principles of differentiation to find tangents in polar co-ordinates, and inequalties?
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- Thread Starter
- 28-06-2004 20:05
- 28-06-2004 20:47
differentation and tangents and polars
ok basically, you have two that you use; tangents parallel and perpendicular to the initial line.
for tangents parallel, u can work them out using d/dt(rsint) = 0
so, whatever the equation of the curve u times by sint, differentiate and put equal to 0 (for stationary points).
then work out the values of t and r, accordingly.
for tangents perpendicular you use d/dt(rcost) = 0
ok there are two ways to do these; graphically and algebraically.
use graphical for modulus graphs
so, draw the graphs, find the intersections and work out the inequalities
for other graphs use algebra
sort the inequality to one fraction or whatever and find the critical values, that is, where y = 0.
then you need to compare the ranges of critical values
so say you have x = -1, 0, 4 as your critical values, the possible ranges of values of x are
x<-1, -1<x<0, 0<x<4 and x>4
use values in these ranges to work out whether the graph is positive or negative in each of these ranges and depending on what youre looking for, choose the appropriate ranges
say you were looking for y>0 [it will always be > or < 0, because you would have taken the other side into y(x)]
then every range that is +ve, those are the ranges you are looking for