Mathematica Solve function gives incorrect solution, why?

Question

Please look into attached file. I’m using Mathematica Solve function to solve some simple equations from physics. One of the equations is an If function which defines function value when a condition is met. Solve finds almost correct solution which itself is a ConditionalExpression. For independent variable θ = 90° the answer given by Solve is in error. It seems that Solve forgets the case when Cos equals 0. Why? Thanks.

Regards/Mikael

mixing inherently symbolic operations Solve with a bunch of floating point values in the input should usually be avoided. Try this without specifying W,u and use Reduce instead of Solve — agentp

Chris Degnen Chris Degnen · Accepted Answer · 2016-04-01T08:51:43

Specifying theta as a real solves the problem.

w = 1500;
mus = 0.4;
fv = f Cos[theta Degree];
fh = f Sin[theta Degree];
fn = fv + w;
ff = If[mus fn >= 0, mus fn, 0];
frul = Quiet@Solve[fh == ff, f, Reals];
f /. frul /. theta -> 90.

{600.}

f /. frul /. theta -> 90

{Undefined}

Same again, with radians.

w = 1500;
mus = 0.4;
fv = f Cos[theta];
fh = f Sin[theta];
fn = fv + w;
ff = If[mus fn >= 0, mus fn, 0];
frul = Quiet@Solve[fh == ff, f, Reals];
f /. frul /. theta -> N[Pi/2]

{600.}

f /. frul /. theta -> Pi/2

{Undefined}

Mathematica Solve function gives incorrect solution, why?

2 Answers