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The Maxima on-line user's manual

Algebra Calculator

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Trigreduce Calculator

Trigreduce

Function: trigreduce (<expr>, <x>)

assume (theta_1 > -%pi/2, theta_2 > -%pi/2, theta_1 < %pi/2, theta_2 < %pi/2);
c1 : cos(theta_1);
 c2 : cos(theta_2);
 s1 : sin(theta_1);
 s2 : sin(theta_2);
trigsimp ((s2^2 + (s2*c1)^2 + (c1*c2)^2) );
ratsimp( (c1^2 * c2) / (s1*c1*c2 + c1^2*c2+s2*(c1^2-s1) ) );
trigreduce( (c1^2 * c2) / (s1*c1*c2 + c1^2*c2+s2*(c1^2-s1) ) );
radcan( (c1^2 * c2) / (s1*c1*c2 + c1^2*c2+s2*(c1^2-s1) ) );
plot3d(cos(theta_1)^2 + sin(theta_2)^2, [theta_1, -%pi/2, %pi/2], [theta_2, -%pi/2, %pi/2]);

Function: trigreduce (<expr>) Combines products and powers of trigonometric and hyperbolic sins and coss of <x> into those of multiples of <x>. It also tries to eliminate these functions when they occur in denominators. If <x> is omitted then all variables in <expr> are used.

See also poissimp.

          (%i1) trigreduce(-sin(x)^2+3*cos(x)^2+x);
                         cos(2 x)      cos(2 x)   1        1
          (%o1)          -------- + 3 (-------- + -) + x - -
                            2             2       2        2

(%o1)                                true
(%i2) 

Trigreduce Example

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