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acos-float-load-sqrt

load(vect);

B:[480,0,600];

D:[0,510,280];

Calculate

acos-integrate

integrate(acos(x),x,0...

Calculate

acos-load-sqrt

load(vect);

R:[0,510,280]-[480,0,...

S:[210,400,0]-[480,0,...

Calculate

acos-draw-draw3d-float-load-pi-sqrt
draw3d(key="u",color="black",vector(p,u),vector(r,u),key="u",color="brown",vector(p,v),vector(q,v));

p:[0,3,0];

q:[2,3,2];

r:[-2,2,3];

Calculate

acos-float-matrix

u:matrix([-3.37535585...

v:matrix([-3.41400263...

w:matrix([1.25741968,...

Calculate

acos-sqrt

peu(x1,y1,z1,x2,y2,z2...

modulo(x,y,z):=sqrt(p...

P1:peu(2,1,0,3,-1,2);

Calculate

acos-sqrt

u:[2,1,0];

v:[3,-1,2];

w:[4,0,3];

Calculate

acos-float-sqrt

pe(x1,y1,z1,x2,y2,z2)...

pe1:pe(-20,3,6,3,12,4);

pe2:pe(3,12,4,-20,3,6);

Calculate

acos-float-sqrt

pe(x1,y1,z1,x2,y2,z2)...

modulo(x,y,z):=sqrt(p...

peuv:pe(-1,2,a,4,a,-3);

Calculate

acos-sqrt

a1 = acos (sqrt(5.0)/...

peu (x1,y1,z1,x2,y2,z...

modulo (x,y,z):= sqrt...

Calculate

acos

Run Example
(%i1)a:1;
(%o1)                                  1
(%i2) b:sqrt(2);
(%o2)                               sqrt(2)
(%i3) diff(asin(x),x) ;
                                      1
(%o3)                            ------------
                                           2
                                 sqrt(1 - x )
(%i4) diff(acos(x),x) ;
                                       1
(%o4)                           - ------------
                                            2
                                  sqrt(1 - x )
(%i5) diff(atan(x),x) ;
                                      1
(%o5)                               ------
                                     2
                                    x  + 1
(%i6) c:diff(asin(x)+acos(x),x);
(%o6)                                  0
(%i7) taylor(cos(x),x,0,5) ;
                                   2    4
                                  x    x
(%o7)/T/                      1 - -- + -- + . . .
                                  2    24
(%i8) taylor(log(1+x)/sin(x),x,0,5) ;
                            2    3       4        5
                       x   x    x    11 x    157 x
(%o8)/T/           1 - - + -- - -- + ----- - ------ + . . .
                       2   2    3     40      720
(%i9) taylor(atanh(x),x,0,4) ;
                                     3
                                    x
(%o9)/T/                        x + -- + . . .
                                    3
(%i10) limit((1+(1/n))^n,n,inf);
(%o10)                                %e
(%i11) 
Run Example
peu(x1,y1,z1,x2,y2,z2):=x1*x2+y1*y2+z1*z2;
(%o1)        peu(x1, y1, z1, x2, y2, z2) := x1 x2 + y1 y2 + z1 z2
(%i2) modulo(x,y,z):=sqrt(peu(x,y,z,x,y,z));
(%o2)           modulo(x, y, z) := sqrt(peu(x, y, z, x, y, z))
(%i3) mo1:modulo(2,1,0);
(%o3)                               sqrt(5)
(%i4) mo2:modulo(3,-1,2);
(%o4)                              sqrt(14)
(%i5) mo3:modulo(4,0,3);
(%o5)                                  5
(%i6) P1:[3,-1,2].[4,0,3];
(%o6)                                 18
(%i7) 	P2:peu(3,-1,2,3,-1,2);
(%o7)                                 14
(%i8) P3:peu(4,0,3,4,0,3);
(%o8)                                 25
(%i9) P4:mo2*mo3;
(%o9)                             5 sqrt(14)
(%i10) P1/P4;
                                      18
(%o10)                            ----------
                                  5 sqrt(14)
(%i11) acos(P1/P4);
                                        18
(%o11)                         acos(----------)
                                    5 sqrt(14)
(%i12) 
Run Example
u:matrix([-4.10905616, 0.39424967, 0.56981468]);
(%o1)              [ - 4.10905616  0.39424967  0.56981468 ]
(%i2) v:matrix([-1.72180528, 2.75235765, 2.61235105]);
(%o2)              [ - 1.72180528  2.75235765  2.61235105 ]
(%i3) w:matrix([4.00658351, -0.74800985, -0.86731420]);
(%o3)              [ 4.00658351  - 0.74800985  - 0.8673142 ]
(%i4) f:matrix([0.48962238, -4.06209668, 0.79000290]);
(%o4)               [ 0.48962238  - 4.06209668  0.7900029 ]
(%i5) acos(float(u.v)/(sqrt((-4.10905616)^2+0.39424967^2+0.56981468^2))*(sqrt((-1.72180528)^2+2.75235765^2+2.61235105^2)));
(%o5)                        2.957270656211434 %i
(%i6) n:matrix([0, 0, 1]);
(%o6)                             [ 0  0  1 ]
(%i7) acos(float(f.n)/(sqrt(0.48962238^2+(-4.06209668)^2+0.79000290^2))*(sqrt(0^2+0^2+1^2)));
(%o7)                          1.380059521380136
(%i8) e:matrix([0, 1, 0]);
(%o8)                             [ 0  1  0 ]
(%i9) acos(float(w.e)/(sqrt(4.00658351^2+(-0.74800985)^2+(-0.86731420)^2))*(sqrt(0^2+1^2+0^2)));
(%o9)                          1.751279613263834
(%i10) vc:299792458/1000*6378137;
                                956058684345373
(%o10)                          ---------------
                                      500
(%i11) e1:(x-(-4.10905616))^2+(y-0.39424967)^2+(z-0.56981468)^2=vc^2*(t-95.596783)^2;
                       2                   2                   2
(%o11) (z - 0.56981468)  + (y - 0.39424967)  + (x + 4.10905616)  = 
                                                                              2
                                914048207912205567857546509129 (t - 95.596783)
                                -----------------------------------------------
                                                    250000
(%i12) e2:(x-(-1.72180528))^2+(y-2.75235765)^2+(z-2.61235105)^2=vc^2*(t-78.639967)^2;
                       2                   2                   2
(%o12) (z - 2.61235105)  + (y - 2.75235765)  + (x + 1.72180528)  = 
                                                                              2
                                914048207912205567857546509129 (t - 78.639967)
                                -----------------------------------------------
                                                    250000
(%i13) e3:(x-4.00658351)^2+(y-(-0.74800985))^2+(z-(-0.86731420))^2=vc^2*(t-91.675562)^2;
                      2                   2                   2
(%o13) (z + 0.8673142)  + (y + 0.74800985)  + (x - 4.00658351)  = 
                                                                              2
                                914048207912205567857546509129 (t - 91.675562)
                                -----------------------------------------------
                                                    250000
(%i14) e4:(x-0.48962238)^2+(y-(-4.06209668))^2+(z-0.79000290)^2=vc^2*(t-108.257901)^2;
                      2                   2                   2
(%o14) (z - 0.7900029)  + (y + 4.06209668)  + (x - 0.48962238)  = 
                                                                              2
                               914048207912205567857546509129 (t - 108.257901)
                               ------------------------------------------------
                                                    250000
(%i15) l1:e2-e1;
                         2                   2                   2
(%o15) - (z - 0.56981468)  + (z - 2.61235105)  - (y - 0.39424967)
                   2                   2                   2
 + (y - 2.75235765)  - (x + 4.10905616)  + (x + 1.72180528)  = 
                                              2
914048207912205567857546509129 (t - 78.639967)
-----------------------------------------------
                    250000
                                                 2
   914048207912205567857546509129 (t - 95.596783)
 - -----------------------------------------------
                       250000
(%i16) l2:e3-e1;
                      2                   2                   2
(%o16) (z + 0.8673142)  - (z - 0.56981468)  + (y + 0.74800985)
                   2                   2                   2
 - (y - 0.39424967)  - (x + 4.10905616)  + (x - 4.00658351)  = 
                                              2
914048207912205567857546509129 (t - 91.675562)
-----------------------------------------------
                    250000
                                                 2
   914048207912205567857546509129 (t - 95.596783)
 - -----------------------------------------------
                       250000
(%i17) l3:e4-e1;
                         2                  2                   2
(%o17) - (z - 0.56981468)  + (z - 0.7900029)  + (y + 4.06209668)
                   2                   2                   2
 - (y - 0.39424967)  - (x + 4.10905616)  + (x - 0.48962238)  = 
                                               2
914048207912205567857546509129 (t - 108.257901)
------------------------------------------------
                     250000
                                                 2
   914048207912205567857546509129 (t - 95.596783)
 - -----------------------------------------------
                       250000
(%i18) linsolve:([l1,l2,l3],[x,y,z,t]);
(%o18)                           [x, y, z, t]
(%i19) 

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