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# How do I solve inequalities with conditional expression (variables)?

Posted 10 years ago
 Hi Dear Community, Want to solve the inequality: -Cos[omega] Cos[psi] Sin[phi] + Sin[omega] Cos[phi] >= 0  where I have conditional expressions: s - u= 0, s - u <= psi <= s + u && t - u <= phi <= t + u]  so for omega=0.1, I write: test[0.1] Eventually I want to make such a function test[omega,i]:=Table[ Simplify[-Cos[omega] Cos[psi] Sin[phi] + Sin[omega] Cos[phi] >= 0, s - u <= psi <= s + u && t - u <= phi <= t + u],{i,1,imax}]  The problem: The boundaries for phi and psi are not numbers and therefore there are problems evaluating it. Sorry if I am not completely clear and thanks for any help.
 I notices something more:If I choose omega=0 therefore Table[test[0, s[i], t[i], u[i]], {i, 1, 5}] he gives me outputs that such as True,FalseBut if omega is anything else then 0,Pi/2 and I run: test[omega_, psiFix_, phiFix_, delta_] := FullSimplify[-Cos[omega] Cos[psi] Sin[phi] + Sin[omega] Cos[phi] >= 0, psiFix - delta < psi < psiFix + delta && phiFix - delta < phi < phiFix + delta] Table[test[0.1, s[i], t[i], u[i]], {i, 1, 5}] I get such crappy outputs: {1. Cos[phi] >= 9.96664 Cos[psi] Sin[phi], 1. Cos[phi] >= 9.96664 Cos[psi] Sin[phi], 1. Cos[phi] >= 9.96664 Cos[psi] Sin[phi], 1. Cos[phi] >= 9.96664 Cos[psi] Sin[phi], 1. Cos[phi] >= 9.96664 Cos[psi] Sin[phi]}