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asin-diff-phi-sqrt

theta: sqrt(x*x+y*y);

phi: asin(x/theta);

diff(theta)^+sin(thet...

Calculate

asin-constant-cos-declare-diff-phi-plot2d-sqrt
plot2d (c(t), [t, 0, t[f]]);

RPM:200;

t[f]:60/RPM;

theta(t):=%pi/30*RPM*t;

Calculate

asin-atan-sqrt

r:sqrt((0.02451247265...

LA:asin(- 0.831421512...

LO:atan(- 0.466098894...

Calculate

asin-ident-mat_norm-matrix-sqrt-transpose

/* "Ground truth" */R...

RBTruth : transpose(m...

RCTruth : transpose(m...

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asin-atan-expand-float-linsolve-pi-rhs-sqrt-time

c:299792458;

rt:6378137;

vc:(c/(1000*rt));

Calculate

asin-sin

sin(asin(a));

Calculate

asin-diff-plot2d
plot2d([exp^asin(x),diff(exp^asin(x),x,2),diff(exp^asin(x),x,1)],[x,0,10]);

plot2d([exp^asin(x),d...

Calculate

asin-diff

diff((asin(x))^2,x);

Calculate

asin-atan-expand-float-linsolve-pi-rhs-sqrt-time

c:299792458;

rt:6378137;

vc:(c/(1000*rt));

Calculate

asin

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
taylor(asin(x),x,0,20);
              3      5      7       9       11        13        15         17
             x    3 x    5 x    35 x    63 x     231 x     143 x     6435 x
(%o1)/T/ x + -- + ---- + ---- + ----- + ------ + ------- + ------- + --------
             6     40    112    1152     2816     13312     10240     557056
                                                                     19
                                                              12155 x
                                                            + --------- + . . .
                                                               1245184
(%i2) plot2d([taylor(asin(x),x,0,4), asin(x)],[x,-1,1],[y,-1.5,1.5]);
plotplot2d([taylor(asin(x),x,0,4), asin(x)],[x,-1,1],[y,-1.5,1.5]);float(3/40);
(%o3)                                0.075
(%i4) float(5/112);
(%o4)                          0.044642857142857
(%i5) float(35/1152);
(%o5)                          0.030381944444444
(%i6) float(63/2816);
(%o6)                          0.022372159090909
(%i7) float(231/13312);
(%o7)                          0.017352764423077
(%i8) float(143/10240);
(%o8)                            0.01396484375
(%i9) float(6435/557056);
(%o9)                          0.01155180089614
(%i10) 
Run Example
sin((%pi)/6);
                                       1
(%o1)                                  -
                                       2
(%i2) cos((%pi)/6);
                                    sqrt(3)
(%o2)                               -------
                                       2
(%i3) tan((%pi)/6);
                                       1
(%o3)                               -------
                                    sqrt(3)
(%i4) sec((%pi)/6);
                                       2
(%o4)                               -------
                                    sqrt(3)
(%i5) cot((%pi)/6);
(%o5)                               sqrt(3)
(%i6) asin((%pi)/6);
                                        %pi
(%o6)                              asin(---)
                                         6
(%i7) acos((%pi)/6);
                                        %pi
(%o7)                              acos(---)
                                         6
(%i8) atan((%pi)/6);
                                        %pi
(%o8)                              atan(---)
                                         6
(%i9) asec((%pi)/6);
                                        %pi
(%o9)                              asec(---)
                                         6
(%i10) acot((%pi)/6);
                                        %pi
(%o10)                             acot(---)
                                         6
(%i11) 
[abs,acos,asin,atan2,expand,float,linsolve,matrix,pi,rhs,sqrt,time] [abs,acos,asin,expand,float,linsolve,matrix,pi,rhs,sqrt,time] [abs,asin,atan,plot2d] [abs,asin,diff,numer] [abs,asin,do,numer,print,while] [acos,asin,atan,expand,float,linsolve,matrix,pi,rhs,sqrt,time] [acos,asin,atan2,expand,float,linsolve,matrix,pi,rhs,sqrt,time] [acos,asin,atan2,expand,float,linsolve,matrix,pi,rhs,sqrt] [acos,asin,float,plot3d,sin] [acos,asin,jacobian,sqrt] [acos,asin,plot2d] [acos,asin,plot3d,sin,sqrt] [args,asin,atan2,block,cos,flatten,float,ident,length,make_random_state,makelist,matrix,set_random_state,sin,sqrt,subst,transpose] [args,asin,atan2,block,cos,flatten,float,ident,length,make_random_state,makelist,matrix,set_random_state,sin,sqrt,transpose] [args,asin,atan2,block,cos,flatten,float,ident,length,make_random_state,makelist,set_random_state,sqrt] [asin,atan,beta,gamma,numer,sqrt] [asin,atan,cos,diff,phi,plot2d,sqrt] [asin,atan,cos,diff,sin] [asin,atan,cos,phi,plot2d,sqrt] [asin,atan,expand,float,linsolve,matrix,pi,rhs,sqrt,time] [asin,atan,expand,float,linsolve,matrix,rhs,sqrt,time] [asin,atan,expand,float,linsolve,pi,rhs,sqrt,time] [asin,atan,expand,float,linsolve,rhs,sqrt,time] [asin,atan,matrix,sqrt] [asin,atan,sqrt] [asin,atan2,beta,cos,float,gamma,matrix,sin] [asin,beta,cos,float,gamma,matrix,sin] [asin,beta,delta,float,gamma,sin] [asin,constant,cos,declare,diff,phi,plot2d,sqrt] [asin,cos,diff,solve,sqrt] [asin,cos,plot2d,sqrt,tan] [asin,cos,plot3d] [asin,cos,solve] [asin,cos,sqrt,tan] [asin,diff,plot2d] [asin,diff] [asin,float,ident,mat_norm,matrix,max,sqrt,transpose] [asin,float,ident,mat_norm,matrix,sqrt,transpose] [asin,float,pi] [asin,float] [asin,integrate,log,sin,sqrt] [asin,integrate,sqrt] [asin,integrate] [asin,plot2d,taylor] [asin,plot2d] [asin,sin,sqrt] [asin,sin] [asin,solve] [asin,taylor] [asin]

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