The following inverse trigonometric functions simplify to an angle displayed in the angular unit (degrees or radians) specified by the Angular Unit fieldAngular_Unit_field of the Options > Mode Settings > Simplification command19_L5FP.  However, the these functions always approximate to an angle in radians.  The following discussion assumes the angular unit is a radian.


ATAN(z) is the principal arctangent of z (i.e. the angle whose tangent is z).  ATAN(y, x) is the angle of the point (x, y) in the x-y plane measured counterclockwise from the positive x-axis.  ATAN(y, x) function simplifies to an equivalent expression using the single-argument ATAN function.


Note that the order of the arguments to ATAN(y, x) is opposite to the usual coordinate pair order.  You can remember this by noting that ATAN(y, x) equals ATAN(y/x) if x is positive.  If x is real, than ATAN(x) lies in the closed-interval [-π/2, π/2].  If x and y are real, then ATAN(y, x) lies in the interval (-π, π].


ACOT(z) is the principal arccotangent of z (i.e. the angle whose cotangent is z).  ACOT(x, y) is the angle of the point (x, y).  ACOT(z) simplifies to π/2 - ATAN(z).  ACOT(x, y) simplifies to ATAN(y, x), which is further transformed as described above.  If x is real, then ACOT(x) lies in the closed-interval [0, π].  If x and y are real, then ACOT(x, y) lies in the interval (-π, π].


ASIN(z) is the principal arcsine of z.  If x is in the interval [-1, 1], then ASIN(x) lies in the closed-interval [-π/2, π/2].


ACOS(z) is the principal arccosine of z.  ACOS(z) simplifies to π/2 - ASIN(z) which is further transformed as described above.  If x is in the interval [-1, 1], then ACOS(x) lies in the closed-interval [0, π].


ASEC(z) is the arcsecant of z.  ASEC(z) simplifies to ACOS(1/z), which is further transformed as described above.


ACSC(z) is the arccosecant of z.  ACSC(z) is replaced by ASIN(1/z), which is further transformed as described above.


Unlike the above inverse trigonometric functions, the following functions always simplify and approximate to an angle expressed in degrees:

ARCSIN(z) returns the principal arcsine of z expressed in degrees.

ARCCOS(z) returns the principal arccosine of z expressed in degrees.

ARCTAN(z) returns the principal arctangent of z expressed in degrees.  ARCTAN(y,x) returns the angle of the point (x,y) expressed in degrees and measured counterclockwise from the positive x-axis.

ARCCOT(z) returns the principal arccotangent of z expressed in degrees.  ARCCOT(y,x) returns the angle of the point (x,y) expressed in degrees and measured counterclockwise from the positive x-axis.

ARCSEC(z) returns the principal arcsecant of z expressed in degrees.

ARCCSC(z) returns the principal arccosecant of z expressed in degrees.


Other Built-in Functions and ConstantsBuilt_in_Functions_and_Constants 

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