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Functions and commands 335
Tangent
atanx → asinx Returns an expression with atan(x) rewritten as:
atan2asin(Expr)
Example:
atan2asin(atan(2*x)) returns
atanx → acosx Returns an expression with atan(x) rewritten as:
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)) returns
Trig
trigx → sinx Returns an expression simplified using the formulas
sin(x)^2+cos(x)^2=1 and tan(x)=sin(x)/cos(x). Sin(x) is given
precedence over cos(x) and tan(x) in the result.
trigsin(Expr)
Example:
trigsin(cos(x)^4+sin(x)^2) returns sin(x)^4-
sin(x)^2+1
x
1 x
2
–
--------------------
asin
2 x
12x
2
–
---------------------------------
asin
2
---
x
1 x
2
+
--------------------
acos–
2
x
2
---
tan
x
2
---
2
tan 1+
--------------------------------