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atan-diff-solve

f: atan(x)+(1-x)/(1+x...

df: diff(f,x);

solve(df=0,x);

Calculate

atan-plot2d
plot2d(atan(x/5),[x,-10,10]);

plot2d(atan(x/5),[x,-...

Calculate

atan-realpart

realpart(5*%e^(%i*ata...

Calculate

atan-plot2d-sqrt
plot2d(atan(sqrt(x^2*(2-x^2))/(1-x^2)),[x,0,1]);

plot2d(atan(sqrt(x^2*...

Calculate

atan-define

define(I(S,X),(S+4*X^...

define(Q(S,X),2*X*(1-...

define(theta(I,Q),ata...

Calculate

atan-cos-expand

expand(cos(2*%pi/3)-a...

Calculate

atan-tan

atan((1+0.5)^0.5*tan(...

Calculate

atan-diff

U:(1/4)*(5*y^2+2*y-5)...

A:[x=1,y=1];

diff(U,x);

Calculate

atan-beta-numer

a:20;

b:16;

beta:atan(b/a);

Calculate

atan-logarc-logcontract-ratsimp-rhs-tan-trigsimp

mf:1=tan(atan(1/2)+at...

trigsimp(rhs(mf));

logarc(rhs(mf));

Calculate

atan

Run Example
(%i1)rt:tan(atan(1/2)+atan(1/3))=1;
                                   1         1
(%o1)                     tan(atan(-) + atan(-)) = 1
                                   2         3
(%i2) trigsimp(lhs(rt));
                                     1         1
                            sin(atan(-) + atan(-))
                                     2         3
(%o2)                       ----------------------
                                     1         1
                            cos(atan(-) + atan(-))
                                     2         3
(%i3)  logarc(lhs(rt));
                    %i                %i             %i                %i
            %i (log(-- + 1) - log(1 - --))   %i (log(-- + 1) - log(1 - --))
                    2                 2              3                 3
(%o3) - tan(------------------------------ + ------------------------------)
                          2                                2
(%i4) ratsimp(%);
(%o4)             
Run Example
th: atan(.113/114.014);
(%o1)                        9.9110603084150823E-4
(%i2) rot1: matrix([cos(th),-sin(th)],[sin(th),cos(th)]);
              [   0.99999950885446     - 9.9110586858239995E-4 ]
(%o2)         [                                                ]
              [ 9.9110586858239995E-4     0.99999950885446     ]
(%i3) v1: matrix([-17.889],[-.065]);
                                 [ - 17.889 ]
(%o3)                            [          ]
                                 [ - 0.065  ]
(%i4) v2: matrix([-18.013],[13.957]);
                                 [ - 18.013 ]
(%o4)                            [          ]
                                 [  13.957  ]
(%i5) v3: matrix([-.113],[14.014]);
                                  [ - 0.113 ]
(%o5)                             [         ]
                                  [ 14.014  ]
(%i6) v1p: rot1.v1;
                            [ - 17.88892679201594 ]
(%o6)                       [                     ]
                            [ - 0.08272986095861  ]
(%i7) v2p: rot1.v2;
                            [ - 18.02682401760316 ]
(%o7)                       [                     ]
                            [  13.9391403550709   ]
(%i8) v3p: rot1.v3;
                            [ - 0.12688930214287 ]
(%o8)                       [                    ]
                            [ 14.01388112212322  ]
(%i9) 
Run Example
integrate((2*10/PI*atan(cot(PI*50*t)))^2,t,0,10);
                                                                         2
                  2 cos(500 PI)                 cos(500 PI)    2500000 PI
      400 (10 atan (-----------) + 5000 PI atan(-----------) + -----------)
                    sin(500 PI)                 sin(500 PI)         3
(%o1) ---------------------------------------------------------------------
                                         2
                                       PI
(%i2) 

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