[SPARK-23329][SQL] Fix documentation of trigonometric functions

## What changes were proposed in this pull request?

Provide more details in trigonometric function documentations. Referenced `java.lang.Math` for further details in the descriptions.
## How was this patch tested?

Ran full build, checked generated documentation manually

Author: Mihaly Toth <[email protected]>

Closes apache#20618 from misutoth/trigonometric-doc.

(cherry picked from commit a366b95)
Signed-off-by: hyukjinkwon <[email protected]>

Author: misutoth

R/pkg/R/functions.R

@@ -278,8 +278,8 @@ setMethod("abs",
           })
 
 #' @details
-#' \code{acos}: Computes the cosine inverse of the given value; the returned angle is in
-#' the range 0.0 through pi.
+#' \code{acos}: Returns the inverse cosine of the given value,
+#' as if computed by \code{java.lang.Math.acos()}
 #'
 #' @rdname column_math_functions
 #' @export
@@ -334,8 +334,8 @@ setMethod("ascii",
           })
 
 #' @details
-#' \code{asin}: Computes the sine inverse of the given value; the returned angle is in
-#' the range -pi/2 through pi/2.
+#' \code{asin}: Returns the inverse sine of the given value,
+#' as if computed by \code{java.lang.Math.asin()}
 #'
 #' @rdname column_math_functions
 #' @export
@@ -349,8 +349,8 @@ setMethod("asin",
           })
 
 #' @details
-#' \code{atan}: Computes the tangent inverse of the given value; the returned angle is in the range
-#' -pi/2 through pi/2.
+#' \code{atan}: Returns the inverse tangent of the given value,
+#' as if computed by \code{java.lang.Math.atan()}
 #'
 #' @rdname column_math_functions
 #' @export
@@ -613,7 +613,8 @@ setMethod("covar_pop", signature(col1 = "characterOrColumn", col2 = "characterOr
           })
 
 #' @details
-#' \code{cos}: Computes the cosine of the given value. Units in radians.
+#' \code{cos}: Returns the cosine of the given value,
+#' as if computed by \code{java.lang.Math.cos()}. Units in radians.
 #'
 #' @rdname column_math_functions
 #' @aliases cos cos,Column-method
@@ -627,7 +628,8 @@ setMethod("cos",
           })
 
 #' @details
-#' \code{cosh}: Computes the hyperbolic cosine of the given value.
+#' \code{cosh}: Returns the hyperbolic cosine of the given value,
+#' as if computed by \code{java.lang.Math.cosh()}.
 #'
 #' @rdname column_math_functions
 #' @aliases cosh cosh,Column-method
@@ -1463,7 +1465,8 @@ setMethod("sign", signature(x = "Column"),
           })
 
 #' @details
-#' \code{sin}: Computes the sine of the given value. Units in radians.
+#' \code{sin}: Returns the sine of the given value,
+#' as if computed by \code{java.lang.Math.sin()}. Units in radians.
 #'
 #' @rdname column_math_functions
 #' @aliases sin sin,Column-method
@@ -1477,7 +1480,8 @@ setMethod("sin",
           })
 
 #' @details
-#' \code{sinh}: Computes the hyperbolic sine of the given value.
+#' \code{sinh}: Returns the hyperbolic sine of the given value,
+#' as if computed by \code{java.lang.Math.sinh()}.
 #'
 #' @rdname column_math_functions
 #' @aliases sinh sinh,Column-method
@@ -1653,7 +1657,9 @@ setMethod("sumDistinct",
           })
 
 #' @details
-#' \code{tan}: Computes the tangent of the given value. Units in radians.
+#' \code{tan}: Returns the tangent of the given value,
+#' as if computed by \code{java.lang.Math.tan()}.
+#' Units in radians.
 #'
 #' @rdname column_math_functions
 #' @aliases tan tan,Column-method
@@ -1667,7 +1673,8 @@ setMethod("tan",
           })
 
 #' @details
-#' \code{tanh}: Computes the hyperbolic tangent of the given value.
+#' \code{tanh}: Returns the hyperbolic tangent of the given value,
+#' as if computed by \code{java.lang.Math.tanh()}.
 #'
 #' @rdname column_math_functions
 #' @aliases tanh tanh,Column-method
@@ -1973,7 +1980,8 @@ setMethod("year",
 
 #' @details
 #' \code{atan2}: Returns the angle theta from the conversion of rectangular coordinates
-#' (x, y) to polar coordinates (r, theta). Units in radians.
+#' (x, y) to polar coordinates (r, theta),
+#' as if computed by \code{java.lang.Math.atan2()}. Units in radians.
 #'
 #' @rdname column_math_functions
 #' @aliases atan2 atan2,Column-method

python/pyspark/sql/functions.py

@@ -106,18 +106,15 @@ def _():
 
 _functions_1_4 = {
     # unary math functions
-    'acos': 'Computes the cosine inverse of the given value; the returned angle is in the range' +
-            '0.0 through pi.',
-    'asin': 'Computes the sine inverse of the given value; the returned angle is in the range' +
-            '-pi/2 through pi/2.',
-    'atan': 'Computes the tangent inverse of the given value; the returned angle is in the range' +
-            '-pi/2 through pi/2',
+    'acos': ':return: inverse cosine of `col`, as if computed by `java.lang.Math.acos()`',
+    'asin': ':return: inverse sine of `col`, as if computed by `java.lang.Math.asin()`',
+    'atan': ':return: inverse tangent of `col`, as if computed by `java.lang.Math.atan()`',
     'cbrt': 'Computes the cube-root of the given value.',
     'ceil': 'Computes the ceiling of the given value.',
-    'cos': """Computes the cosine of the given value.
-
-           :param col: :class:`DoubleType` column, units in radians.""",
-    'cosh': 'Computes the hyperbolic cosine of the given value.',
+    'cos': """:param col: angle in radians
+           :return: cosine of the angle, as if computed by `java.lang.Math.cos()`.""",
+    'cosh': """:param col: hyperbolic angle
+           :return: hyperbolic cosine of the angle, as if computed by `java.lang.Math.cosh()`""",
     'exp': 'Computes the exponential of the given value.',
     'expm1': 'Computes the exponential of the given value minus one.',
     'floor': 'Computes the floor of the given value.',
@@ -127,14 +124,16 @@ def _():
     'rint': 'Returns the double value that is closest in value to the argument and' +
             ' is equal to a mathematical integer.',
     'signum': 'Computes the signum of the given value.',
-    'sin': """Computes the sine of the given value.
-
-           :param col: :class:`DoubleType` column, units in radians.""",
-    'sinh': 'Computes the hyperbolic sine of the given value.',
-    'tan': """Computes the tangent of the given value.
-
-           :param col: :class:`DoubleType` column, units in radians.""",
-    'tanh': 'Computes the hyperbolic tangent of the given value.',
+    'sin': """:param col: angle in radians
+           :return: sine of the angle, as if computed by `java.lang.Math.sin()`""",
+    'sinh': """:param col: hyperbolic angle
+           :return: hyperbolic sine of the given value,
+                    as if computed by `java.lang.Math.sinh()`""",
+    'tan': """:param col: angle in radians
+           :return: tangent of the given value, as if computed by `java.lang.Math.tan()`""",
+    'tanh': """:param col: hyperbolic angle
+            :return: hyperbolic tangent of the given value,
+                     as if computed by `java.lang.Math.tanh()`""",
     'toDegrees': '.. note:: Deprecated in 2.1, use :func:`degrees` instead.',
     'toRadians': '.. note:: Deprecated in 2.1, use :func:`radians` instead.',
     'bitwiseNOT': 'Computes bitwise not.',
@@ -173,16 +172,31 @@ def _():
 
 _functions_2_1 = {
     # unary math functions
-    'degrees': 'Converts an angle measured in radians to an approximately equivalent angle ' +
-               'measured in degrees.',
-    'radians': 'Converts an angle measured in degrees to an approximately equivalent angle ' +
-               'measured in radians.',
+    'degrees': """
+               Converts an angle measured in radians to an approximately equivalent angle
+               measured in degrees.
+               :param col: angle in radians
+               :return: angle in degrees, as if computed by `java.lang.Math.toDegrees()`
+               """,
+    'radians': """
+               Converts an angle measured in degrees to an approximately equivalent angle
+               measured in radians.
+               :param col: angle in degrees
+               :return: angle in radians, as if computed by `java.lang.Math.toRadians()`
+               """,
 }
 
 # math functions that take two arguments as input
 _binary_mathfunctions = {
-    'atan2': 'Returns the angle theta from the conversion of rectangular coordinates (x, y) to' +
-             'polar coordinates (r, theta). Units in radians.',
+    'atan2': """
+             :param col1: coordinate on y-axis
+             :param col2: coordinate on x-axis
+             :return: the `theta` component of the point
+                (`r`, `theta`)
+                in polar coordinates that corresponds to the point
+                (`x`, `y`) in Cartesian coordinates,
+                as if computed by `java.lang.Math.atan2()`
+             """,
     'hypot': 'Computes ``sqrt(a^2 + b^2)`` without intermediate overflow or underflow.',
     'pow': 'Returns the value of the first argument raised to the power of the second argument.',
 }