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The function trigfactor factors expresions of form \(\pm \sin x \pm \cos y.\)
Examples:
(%i2) trigfactor(sin(x)+cos(x));
                                            %pi
(%o2)                       sqrt(2) cos(x - ---)
                                             4
(%i3) trigrat(%);
(%o3)                          sin(x) + cos(x)
(%i4) trigfactor(sin(x)+cos(y));
                           y   x   %pi      y   x   %pi
(%o4)                2 cos(- - - + ---) cos(- + - - ---)
                           2   2    4       2   2    4
(%i5) trigrat(%); (%o5) cos(y) + sin(x)
(%i6) trigfactor(sin(x)-cos(3*y));
                         3 y   x   %pi      3 y   x   %pi
(%o6)              2 sin(--- - - + ---) sin(--- + - - ---)
                          2    2    4        2    2    4
(%i7) trigrat(%);
(%o7)                         sin(x) - cos(3 y)
(%i8) trigfactor(-sin(5*x)-cos(3*y));
                        3 y   5 x   %pi      3 y   5 x   %pi
(%o8)           - 2 cos(--- - --- + ---) cos(--- + --- - ---)
                         2     2     4        2     2     4
(%i9) trigrat(%);
(%o9)                      (- cos(3 y)) - sin(5 x)
(%i10) sin(alpha)+sin(beta)=trigfactor(sin(alpha)+sin(beta));
                                       beta   alpha      beta   alpha
(%o10)  sin(beta) + sin(alpha) = 2 cos(---- - -----) sin(---- + -----)
                                        2       2         2       2
(%i11) trigrat(%); (%o78) sin(beta) + sin(alpha) = sin(beta) + sin(alpha)
(%i12) sin(alpha)-sin(beta)=trigfactor(sin(alpha)-sin(beta));
                                        beta   alpha      beta   alpha
(%o12) sin(alpha) - sin(beta) = - 2 sin(---- - -----) cos(---- + -----)
                                         2       2         2       2
(%i13) cos(alpha)+cos(beta)=trigfactor(cos(alpha)+cos(beta));
                                       beta   alpha      beta   alpha
(%o80)  cos(beta) + cos(alpha) = 2 cos(---- - -----) cos(---- + -----)
                                        2       2         2       2
(%i14) cos(alpha)-cos(beta)=trigfactor(cos(alpha)-cos(beta));
                                       beta   alpha      beta   alpha
(%o14)  cos(alpha) - cos(beta) = 2 sin(---- - -----) sin(---- + -----)
                                        2       2         2       2
(%i15) trigfactor(3*sin(x)+7*cos(x)); (%o15) 3 sin(x) + 7 cos(x)
(%i16) c2sin(%);
                                                 7
(%o16)                     sqrt(58) sin(x + atan(-))
                                                 3
(%i17) trigexpand(%),expand; (%o17) 3 sin(x) + 7 cos(x)
10.
(%i18) trigfactor(sin(2*x)); (%o18) sin(2 x) (%i19) trigexpand(%); (%o19) 2 cos(x) sin(x)
Next: Solve Trignometric Equations, Previous: Convert to Hyperbolic Functions, Up: Functions and Variables for trigtools [Contents][Index]