## #math - Thu 22 Mar 2007 between 00:02 and 00:09

### NY Lost Funds

 bsmntbombdood ?ArcCos[x] //TrigToExp% ArcCos[x] //TrigToExp mbot bsmntbombdood: Pi/2 + I*Log[I*x + Sqrt[1 - x^2]] bsmntbombdood neato SeveredCross % Expand cos(3x) mbot SeveredCross: 3*cos*Expand*x SeveredCross Err.% Expand[cos(3x)] mbot SeveredCross: 3*cos*x SeveredCross Aw.That's clearly not right LOL. bsmntbombdood Cos[3*x] SeveredCross Doh, of course.% Expand[Cos[3x]] mbot SeveredCross: Cos[3*x] SeveredCross Aw, it won't give the full expansion. bsmntbombdood hmm% Expand[Cos[x+x]] mbot bsmntbombdood: Cos[2*x] Olathe % Cos[3x] //TrigExpand mbot Olathe: Cos[x]^3 - 3*Cos[x]*Sin[x]^2 bsmntbombdood Olathe to the rescue% Sin[3x] //TrigExpand mbot bsmntbombdood: 3*Cos[x]^2*Sin[x] - Sin[x]^3 bsmntbombdood % Sin[x/3] //TrigExpand mbot bsmntbombdood: Sin[x/3] Olathe % TrigExpand[Cos[3x]] /. Sin[x]->Sqrt[1 - Cos[x]^2] //Expand mbot Olathe: -3*Cos[x] + 4*Cos[x]^3 bsmntbombdood % Solve[y==3*x - 4*x^3, x] mbot bsmntbombdood: {{x -> 1/(2*(-y + Sqrt[-1 + y^2])^(1/3)) + (-y + Sqrt[-1 + y^2])^(1/3)/2}, {x -> -(1 + I*Sqrt[3])/(4*(-y + Sqrt[-1 + y^2])^(1/3)) - ((1 - I*Sqrt[3])*(-y + Sqrt[-1 + y^2])^(1/3))/4}, {x -> -(1 - I*Sqrt[3])/(4*(-y + Sqrt[-1 + y^2])^(1/3)) - ((1 + I*Sqrt[3])*(-y + Sqrt[-1 + y^2])^(1/3))/4}} SeveredCross Yikes.That's uh, very long. cached Solve[D=1/2*c^2*t^2+1/2*c^2*a^2*Log(t),t]% Solve[D=1/2*c^2*t^2+1/2*c^2*a^2*Log(t),t] mbot cached:Set::wrsym: Symbol D is Protected.2 2 2 2