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Functions and commands 333
atanx → acosx Returns an expression with arctan(x) rewritten as pi/2-
arccos(x/sqrt(1+x^2)).
atan2acos(Expr)
tanx → sinx/cosx Returns an expression with tan(x) rewritten as sin(x)/cos(x).
tan2sincos(Expr)
Example:
tan2sincos(tan(x)) gives sin(x)/cos(x)
halftan Returns an expression with sin(x), cos(x) or tan(x) rewritten as
tan(x/2).
halftan(Expr)
Example:
halftan(sin(x)) gives 2*tan(x/2)/(tan(x/2)^2+
Trig
trigx → sinx Returns an expression simplified using the formulas
sin(x)^2+cos(x)^2=1 and tan(x)=sin(x)/cos(x) (privileging
sine).
trigsin(Expr)
Example:
trigsin(cos(x)^4+sin(x)^2) gives sin(x)^4-
sin(x)^2+
trigx → cosx Returns an expression simplified using the formulas
sin(x)^2+cos(x)^2=1 and tan(x)=sin(x)/cos(x) (privileging
cosine).
trigcos(Expr)
Example:
trigcos(sin(x)^4+sin(x)^2) gives cos(x)^4-
3*cos(x)^2+2
trigx → tanx Returns an expression simplified using the formulas
sin(x)^2+cos(x)^2=1 and tan(x)=sin(x)/cos(x) (privileging
tangent).
trigtan(Expr)
Example:
trigtan(cos(x)^4+sin(x)^2) gives
(tan(x)^4+tan(x)^2+1)/(tan(x)^4+2*tan(x)^2+1)