Re: inequations

*To*: mathgroup at smc.vnet.net*Subject*: [mg62847] Re: inequations*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Tue, 6 Dec 2005 23:10:17 -0500 (EST)*Organization*: The Open University, Milton Keynes, UK*References*: <dn368i$2ri$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Norbe wrote: > Can somebody help me with this Inequation? > > (( 2*Sin [a] ) / (3*Pi / 4 ) -a ) +1 -d >= 0 > > I need solve for a, but i can't found any function or easy form for solve. > > > Thank > Hi, An obvious choice would be the function *Reduce*, unfortunately it fails to solve the inequality: In[1]:= expr = ((2*Sin[a])/(3*(Pi/4)) - a) + 1 - d; In[2]:= Reduce[expr >= 0, a] Reduce::nsmet: This system cannot be solved with the methods available to Reduce. More... Out[2]= Reduce[1 - a - d + (8*Sin[a])/(3*Pi) >= 0, a] Therefore, you might be on your own to find a general formula. Studying some particular cases by giving some values to the parameter d and plating the graph of the functions f(a) = 1 - a - d + (8*Sin[a])/(3*Pi) and y = d should help visualizing what's going on (f{a} is decreasing on R and we are interested in the intersection point of f(a) and the horizontal straight line y = d. Then, the required value of a are on the left of the graph). You could try In[3]:= Plot[{expr /. d -> 1, 1}, {a, -10, 10}]; or the following one that gives a family of intersecting curves and their intersection points: In[4]:= Needs["Graphics`Graphics`"] Plot[Evaluate[Table[{expr /. d -> n, n}, {n, -5, 5}]], {a, -10, 10}, PlotStyle -> {{Red}, {Blue, Dashing[{0.015}]}}, ImageSize -> 500, Frame -> True, FrameTicks -> {UnitScale[-3*Pi, 3*Pi, 8/(3*Pi)], Automatic, None, None}, Axes -> None, Epilog -> {PointSize[0.015], Point /@ Table[{a /. FindRoot[expr == n /. d -> n, {a, -n}], n}, {n, -5, 5}]}]; Hope this helps, /J.M.