### Related

u:[1,4,3];

v:[1,-2,4];

u*v;

Calculate

##### acos-float-pi

float(2/%pi);

acos(0.99999997) * 2/...

cos(1.5e-4/(2/%pi));

Calculate

##### acos-asin-plot3d-sin-sqrt

hav(x):=sin(x/2)^2;

ahav(x):=2*asin(sqrt(...

coss(x):=1-2*hav(x);

Calculate

p:[0,3,0];

q:[2,3,2];

r:[-2,2,3];

Calculate

##### acos-expand-float-linsolve-matrix-rhs-sqrt-time

u:matrix([-4.10905616...

v:matrix([-1.72180528...

w:matrix([4.00658351,...

Calculate

##### acos-asin-atan2-expand-float-linsolve-matrix-pi-rhs-sqrt

S1 : matrix([4.088894...

S2 : matrix([3.249530...

S3 : matrix([-3.75759...

Calculate

##### acos-sin-sqrt

OC:sqrt(XC^2+YC^2);

COX:acos(XC/OC);

AOC:acos((Rpo^2+OC^2-...

Calculate

AC:[-2.4,0.8,1.2];

AB:[-2.4,-1.8,0];

Calculate

##### acos-float-matrix-sqrt

u:matrix([-4.10905616...

v:matrix([-1.72180528...

w:matrix([4.00658351,...

Calculate

##### acos-taylor

taylor(acos(x),x,0,8);

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
```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) ```
Run Example
```S1 : matrix([4.08889477, 0.39840116, 0.69762467]);
(%o1)               [ 4.08889477  0.39840116  0.69762467 ]
(%i2) S2 : matrix([3.24953032, -1.52906805, -2.11352020]);
(%o2)              [ 3.24953032  - 1.52906805  - 2.1135202 ]
(%i3) S3 : matrix([-3.75759016, -1.79818707, -0.10725440]);
(%o3)             [ - 3.75759016  - 1.79818707  - 0.1072544 ]
(%i4) S4 : matrix([-1.32228741, -0.56859420, 3.91059084]);
(%o4)              [ - 1.32228741  - 0.5685942  3.91059084 ]
(%i5) N : matrix([0, 0, 1]);
(%o5)                             [ 0  0  1 ]
(%i6) E : matrix([1, 0, 0]);
(%o6)                             [ 1  0  0 ]
(%i7) Vc : (float (299792458/(1000*6378137)));
(%o7)                          0.047003138690812
(%i8) E1 : (x-3.24953032)^2+(y-0.39840116)^2+(z-0.69762467)^2-(Vc^2*((t-86.202474)^2));
2                   2                   2
(%o8) (z - 0.69762467)  + (y - 0.39840116)  + (x - 3.24953032)
2
- 0.0022092950467877 (t - 86.202474)
(%i9) E2 : (x-4.08889477)^2+(y-1.52906805)^2+(z-2.11352020)^2-(Vc^2*((t-76.746675)^2));
2                   2                   2
(%o9) (z - 2.1135202)  + (y - 1.52906805)  + (x - 4.08889477)
2
- 0.0022092950467877 (t - 76.746675)
(%i10) E3 : (x-3.75759016)^2+(y-1.79818707)^2+(z-0.10725440)^2-(Vc^2*((t-46.799036)^2));
2                   2                   2
(%o10) (z - 0.1072544)  + (y - 1.79818707)  + (x - 3.75759016)
2
- 0.0022092950467877 (t - 46.799036)
(%i11) E4 : (x-1.32228741)^2+(y-0.56859420)^2+(z-3.91059084)^2-(Vc^2*((t-62.385050)^2));
2                  2                   2
(%o11) (z - 3.91059084)  + (y - 0.5685942)  + (x - 1.32228741)
2
- 0.0022092950467877 (t - 62.38505)
(%i12) L1 : E2-E1;
2                  2                   2
(%o12) - (z - 0.69762467)  + (z - 2.1135202)  - (y - 0.39840116)
2                   2                   2
+ (y - 1.52906805)  - (x - 3.24953032)  + (x - 4.08889477)
2                                     2
- 0.0022092950467877 (t - 76.746675)  + 0.0022092950467877 (t - 86.202474)
(%i13) L2 : E3-E1;
2                   2                   2
(%o13) (z - 0.1072544)  - (z - 0.69762467)  - (y - 0.39840116)
2                   2                   2
+ (y - 1.79818707)  - (x - 3.24953032)  + (x - 3.75759016)
2                                     2
- 0.0022092950467877 (t - 46.799036)  + 0.0022092950467877 (t - 86.202474)
(%i14) L3 : E4-E1;
2                   2                   2
(%o14) - (z - 0.69762467)  + (z - 3.91059084)  - (y - 0.39840116)
2                   2                   2
+ (y - 0.5685942)  + (x - 1.32228741)  - (x - 3.24953032)
2                                     2
- 0.0022092950467877 (t - 62.38505)  + 0.0022092950467877 (t - 86.202474)
(%i15) acos(float (S1.S2)/(86.202474*76.746675));
(%o15)                         1.569102889005695
(%i16) ((acos(float (S1.S2)/(86.202474*76.746675)))*180)/float(%pi);
(%o16)                         89.90297316181078
(%i17) acos(float (S4.N)/(62.385050*1));
(%o17)                         1.508070458817599
(%i18) ((acos(float (S4.N)/(62.385050*1)))*180)/float(%pi);
(%o18)                         86.40607249860604
(%i19) acos(float (S3.E)/(46.799036*1));
(%o19)                         1.651174891234327
(%i20) ((acos(float (S3.E)/(46.799036*1)))*180)/float(%pi);
(%o20)                         94.60535250569964
(%i21) expand(L1);
(%o21) - 2.83179106 z - 2.26133378 y - 1.678728899999999 x - 0.04178129978824 t
+ 15.72333983469477
(%i22) expand(L2);
(%o22) 1.18074054 z - 2.79957182 y - 1.01611968 x - 0.17410764079961 t
+ 17.73790265492522
(%i23) expand(L3);
(%o23) - 6.425932339999999 z - 0.34038608 y + 3.85448582 x - 0.10523943374089 t
+ 13.97824655508892
(%i24) linsolve([L1,L2,L3],[x,y,z,t]);

rat: replaced 0.0022092950467877 by 248/112253 = 0.0022092950745192

rat: replaced -86.202474 by -55773/647 = -86.2024729520866

rat: replaced -0.002209295046788 by -248/112253 = -0.002209295074519

rat: replaced -76.746675 by -121183/1579 = -76.7466751108296

rat: replaced -4.08889477 by -15317/3746 = -4.08889482114255

rat: replaced -3.24953032 by -10379/3194 = -3.2495303694427

rat: replaced -1.52906805 by -5234/3423 = -1.52906806894537

rat: replaced -0.39840116 by -2741/6880 = -0.3984011627907

rat: replaced -2.1135202 by -11990/5673 = -2.11352018332452

rat: replaced -0.69762467 by -6197/8883 = -0.6976246763481

rat: replaced 0.0022092950467877 by 248/112253 = 0.0022092950745192

rat: replaced -86.202474 by -55773/647 = -86.2024729520866

rat: replaced -0.002209295046788 by -248/112253 = -0.002209295074519

rat: replaced -46.799036 by -29109/622 = -46.7990353697749

rat: replaced -3.75759016 by -7921/2108 = -3.75759013282732

rat: replaced -3.24953032 by -10379/3194 = -3.2495303694427

rat: replaced -1.79818707 by -18052/10039 = -1.79818707042534

rat: replaced -0.39840116 by -2741/6880 = -0.3984011627907

rat: replaced -0.69762467 by -6197/8883 = -0.6976246763481

rat: replaced -0.1072544 by -1511/14088 = -0.1072544009086

rat: replaced 0.0022092950467877 by 248/112253 = 0.0022092950745192

rat: replaced -86.202474 by -55773/647 = -86.2024729520866

rat: replaced -0.002209295046788 by -248/112253 = -0.002209295074519

rat: replaced -62.38505 by -44231/709 = -62.3850493653032

rat: replaced -3.24953032 by -10379/3194 = -3.2495303694427

rat: replaced -1.32228741 by -4509/3410 = -1.32228739002933

rat: replaced -0.5685942 by -3353/5897 = -0.5685942004409

rat: replaced -0.39840116 by -2741/6880 = -0.3984011627907

rat: replaced -3.91059084 by -17539/4485 = -3.91059085841695

rat: replaced -0.69762467 by -6197/8883 = -0.6976246763481
(%o24) [x = (36123308568200765962496726355896495470787683282807835997197097943\
05953698824461694999634517802535142400 %r1 - 132829072060045148545453155493873\
419241520135853988810447102101934612220759930004248547294598912421373487)/7725\
653169396448291301049994452104420199873380856436976301065708304402853499859980\
0601540777289467611520, y = - (28985997250191872054385367833040336487293949505\
675472387642971940502545232582568026661474062569317580800 %r1 - 29058026432069\
719477166052789145515156478212084166234716565441393851096284712026620540271694\
45155106976877)/39915874708548316171722091638002539504366012467758257710888839\
4929060814097492765636441294015995582659520, z = (3632476782637986771051116583\
231479653431330952422836817958586323585512584185523259081891828673674240 %r1
+ 177540717262363179813682330622421107763355178728229511468941982933784361139020796918440412058640659069
)/2341107021029226754939712119530940733393901024501950598879110820698303894999\
95756971519820537240810944, t = %r1]
(%i25) ```

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