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phi-sin-solve

[r=sin(phi)^2,r^2=x^2...

solve(%,[x,y]);

Calculate

phi-solve-tan

eq1:V=h*pi/3*(R^2+R*r...

solve(eq1,h);

eq2:h=(R-r)/tan(phi);

Calculate

phi-sin-solve

[r=sin(phi)^2,r^2=x^2...

solve(%,[r,x,y]);

Calculate

phi-sinh-taylor

cbar: (1/xi)*sinh(xi*...

taylor(cbar,xi,0,3);

Calculate

phi-sinh-taylor

c: (1/xi)*sinh(xi*phi...

taylor(c, phi, 0, 8);

Calculate

phi-solve-tan

eq1:V=h*pi/3*(R^2+R*r...

eq2:solve(eq1,h);

eq3:h=(R-r)/tan(phi);

Calculate

phi-sqrt

phi(z):= sqrt(105/(2*...

phi(-L/2);

phi(L/2);

Calculate

phi-solve-tan

eq1:V=h*pi/3*(R^2+R*r...

eq2:solve(eq1,h);

eq3:h=(R-r)/tan(phi);

Calculate

phi-sqrt

phi(z):= sqrt(105/(2*...

Calculate

phi

Run Example
(%i1)qe:1.6E-19;
(%o1)                       1.5999999999999999E-19
(%i2) E:1E+4;
(%o2)                               10000.0
(%i3) me:1.67E-27;
(%o3)                       1.6700000000000002E-27
(%i4) d:0.04;
(%o4)                                0.04
(%i5) D:0.10;
(%o5)                                 0.1
(%i6) vox:2.8E+7;
(%o6)                               2.8E+7
(%i7) a:qe*E/me;
(%o7)                       9.5808383233532922E+11
(%i8) t:d/vox;
(%o8)                        1.4285714285714286E-9
(%i9) y:0.5*a*(d/vox)^2;
(%o9)                        9.7763656360747883E-7
(%i10) vx:vox;
(%o10)                              2.8E+7
(%i11) vy:a*d/vox;
(%o11)                         1368.69118905047
(%i12) phi:atan(vy/vx)*180/3.141592654;
(%o12)                        0.0028007224470227
(%i13) h:D*vy/vx;
(%o13)                       4.8881828180373942E-6
(%i14) H:y+h;
(%o14)                       5.865819381644873E-6
(%i15) 
Run Example
w: sqrt(x*x+y*y);
                                       2    2
(%o1)                            sqrt(y  + x )
(%i2) dx: diff(theta*sin(phi));
(%o2)            sin(phi) del(theta) + cos(phi) theta del(phi)
(%i3) 
Run Example
matrix([1, 0, 0], [0, cos(phi),sin(phi)], [0, -sin(phi), cos(phi)]) * matrix([cos(theta), 0, -sin(theta)], [0,1,0], [sin(theta), 0, cos(theta)]) *matrix([cos(psi), sin(psi), 0], [-sin(psi), cos(psi), 0], [0, 0, 1]);
        [ cos(psi) cos(theta)          0                   0          ]
        [                                                             ]
(%o1)   [          0           cos(phi) cos(psi)           0          ]
        [                                                             ]
        [          0                   0          cos(phi) cos(theta) ]
(%i2) 

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