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trigreduce

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trigreduce

Run Example
(%i1)p: trigreduce(sin(3*x));
(%o1)                              sin(3 x)
(%i2) 
Run Example
f(theta):=((cos(theta)^2-sin(theta)*(sin(theta)-zeta))/sqrt(lambda^2-(sin(theta)-zeta)^2));
                          2
                       cos (theta) - sin(theta) (sin(theta) - zeta)
(%o1)      f(theta) := --------------------------------------------
                                      2                      2
                           sqrt(lambda  - (sin(theta) - zeta) )
(%i2) trigreduce(f(theta));
                          sqrt(2) sin(theta) zeta
(%o2) ----------------------------------------------------------------
                   2         2
      sqrt(2 lambda  - 2 zeta  + 4 sin(theta) zeta + cos(2 theta) - 1)
                                     sqrt(2) cos(2 theta)
             + ----------------------------------------------------------------
                            2         2
               sqrt(2 lambda  - 2 zeta  + 4 sin(theta) zeta + cos(2 theta) - 1)
(%i3) plt2d(sublis([lambda=3.5,zeta=0.3],f(theta)),[theta,-%pi,%pi]);
               2
            cos (theta) - (sin(theta) - 0.3) sin(theta)
(%o3) plt2d(-------------------------------------------, [theta, - %pi, %pi])
                                                2
                 sqrt(12.25 - (sin(theta) - 0.3) )
(%i4) 
Run Example
assume (theta_1 >
 -%pi/2, theta_2 >
 -%pi/2, theta_1 <
 %pi/2, theta_2 <
 %pi/2);
                    %pi              %pi  %pi            %pi
(%o1)  [theta_1 > - ---, theta_2 > - ---, --- > theta_1, --- > theta_2]
                     2                2    2              2
(%i2) c1 : cos(theta_1);
(%o2)                            cos(theta_1)
(%i3)  c2 : cos(theta_2);
(%o3)                            cos(theta_2)
(%i4)  s1 : sin(theta_1);
(%o4)                            sin(theta_1)
(%i5)  s2 : sin(theta_2);
(%o5)                            sin(theta_2)
(%i6) trigsimp ((s2^2 + (s2*c1)^2 + (c1*c2)^2) );
                            2               2
(%o6)                    sin (theta_2) + cos (theta_1)
(%i7) ratsimp( (c1^2 * c2) / (s1*c1*c2 + c1^2*c2+s2*(c1^2-s1) ) );
            2                                            2
(%o7) - (cos (theta_1) cos(theta_2))/((sin(theta_1) - cos (theta_1))
                                                      2
     sin(theta_2) + (- cos(theta_1) sin(theta_1) - cos (theta_1)) cos(theta_2))
(%i8) trigreduce( (c1^2 * c2) / (s1*c1*c2 + c1^2*c2+s2*(c1^2-s1) ) );
(%o8) 2 (cos(theta_2 + 2 theta_1)/(4 sin(theta_2 + 2 theta_1)
 + 2 cos(theta_2 + 2 theta_1) + 4 cos(theta_2 + theta_1)
 - 4 cos(theta_2 - theta_1) + 2 cos(theta_2 - 2 theta_1) + 4 sin(theta_2)
 + 4 cos(theta_2)) + cos(theta_2 - 2 theta_1)
/(4 sin(theta_2 + 2 theta_1) + 2 cos(theta_2 + 2 theta_1)
 + 4 cos(theta_2 + theta_1) - 4 cos(theta_2 - theta_1)
 + 2 cos(theta_2 - 2 theta_1) + 4 sin(theta_2) + 4 cos(theta_2)))
 + (2 cos(theta_2))/(2 sin(theta_2 + 2 theta_1) + cos(theta_2 + 2 theta_1)
 + 2 cos(theta_2 + theta_1) - 2 cos(theta_2 - theta_1)
 + cos(theta_2 - 2 theta_1) + 2 sin(theta_2) + 2 cos(theta_2))
(%i9) radcan( (c1^2 * c2) / (s1*c1*c2 + c1^2*c2+s2*(c1^2-s1) ) );
            2                                            2
(%o9) - (cos (theta_1) cos(theta_2))/((sin(theta_1) - cos (theta_1))
                                                      2
     sin(theta_2) + (- cos(theta_1) sin(theta_1) - cos (theta_1)) cos(theta_2))
(%i10) 
[acos,cos,diff,plot2d,sin,solve,subst,trigexpand,trigreduce,trigsimp] [addcol,define,determinant,diff,eigenvectors,exp,imagpart,integrate,invert,matrix,ratsimp,realpart,trigreduce,trigsimp] [addcol,define,determinant,eigenvectors,exp,imagpart,matrix,realpart,trigreduce] [assume,cos,radcan,ratsimp,sin,trigreduce,trigsimp] [assume,cos,radcan,ratsimp,sin,trigreduce] [assume,cos,sin,trigreduce] [atan2,collectterms,cos,expand,float,log,plot2d,sin,tan,trigexpand,trigreduce] [block,cos,diff,expand,horner,ratdisrep,subst,sum,taylor,trigreduce] [block,integrate,phi,ratsimp,sin,subst,taylor,trigreduce] [collectterms,cos,diff,sin,trigreduce] [constant,cos,declare,globalsolve,lhs,multthru,realonly,rhs,sin,trigreduce,true] [cos,cot,diff,expand,ratsimp,sin,sqrt,subst,trigexpand,trigreduce] [cos,diff,divide,ev,first,second,sin,sqrt,third,trigrat,trigreduce] [cos,diff,ev,first,second,sin,sqrt,third,trigrat,trigreduce] [cos,diff,ev,first,second,sqrt,trigrat,trigreduce] [cos,diff,expand,sin,sqrt,subst,tan,trigexpand,trigreduce] [cos,diff,false,sin,trigreduce] [cos,diff,first,second,trigrat,trigreduce] [cos,diff,phi,psi,rhs,sin,solve,subst,trigreduce] [cos,diff,sin,trigreduce,trigsimp] [cos,diff,sin,trigreduce] [cos,display2d,false,sin,solve,trigrat,trigreduce] [cos,display2d,false,sin,solve,trigreduce,trigsimp] [cos,display2d,false,sin,trigexpand,trigreduce,trigsimp] [cos,expand,sin,subst,trigexpand,trigreduce] [cos,expand,sin,trigreduce] [cos,factor,trigreduce] [cos,matrix,sin,trigreduce] [cos,ratsimp,sin,trigreduce] [cos,sin,solve,trigreduce] [cos,sin,sqrt,trigreduce] [cos,sin,subst,trigexpand,trigreduce] [cos,sin,tan,trigreduce] [cos,sin,trigexpand,trigreduce] [cos,sin,trigreduce,trigsimp] [cos,sin,trigreduce] [cos,trigexpand,trigreduce] [cos,trigreduce] [cot,tan,trigexpand,trigreduce] [expand,sin,trigreduce] [linsolve,rhs,sin,trigreduce] [linsolve,sin,trigexpand,trigreduce] [linsolve,sin,trigreduce] [sin,tan,trigreduce,trigsimp] [sin,tan,trigreduce] [sin,trigexpand,trigreduce,trigsimp] [sin,trigexpand,trigreduce] [sin,trigreduce] [sqrt,trigreduce] [trigreduce]

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