From 4c65986502da305641ed34df0aa1032d9134f0fe Mon Sep 17 00:00:00 2001
From: Landon Curt Noll <github-mail@asthe.com>
Date: Mon, 11 Sep 2023 15:34:12 -0700
Subject: [PATCH] improve inverse trigonometric help files

---
 help/acos | 8 +++++++-
 help/acot | 8 ++++++++
 help/acsc | 8 ++++++++
 help/asec | 8 ++++++++
 help/asin | 8 +++++++-
 help/atan | 8 ++++++++
 6 files changed, 46 insertions(+), 2 deletions(-)

diff --git a/help/acos b/help/acos
index 0694ff2..ba7f6ca 100644
--- a/help/acos
+++ b/help/acos
@@ -14,7 +14,13 @@ DESCRIPTION
     Returns the inverse cosine of x to a multiple of eps with error less in
     absolute value than .75 * eps.
 
-    v = acos(x) is the number in [0, pi] for which cos(v) = x.
+    This function is sometimes called arccos, is such that:
+
+	cos(acos(x)) = x
+
+    and such that:
+
+	acos(x) = asrc(1/x)
 
 EXAMPLE
     ; print acos(.5, 1e-5), acos(.5, 1e-10), acos(.5, 1e-15), acos(.5, 1e-20)
diff --git a/help/acot b/help/acot
index a72e991..56ad66e 100644
--- a/help/acot
+++ b/help/acot
@@ -14,6 +14,14 @@ DESCRIPTION
     Returns the inverse cotangent of x to a multiple of eps with error less in
     absolute value than .75 * eps.
 
+    This function is sometimes called arccot, is such that:
+
+	cot(acot(x)) = x
+
+    and such that:
+
+	acot(x) = atan(1/x)
+
 EXAMPLE
     ; print acot(2, 1e-5),  acot(2, 1e-10), acot(2, 1e-15), acot(2, 1e-20)
     0.46365 0.463647609 0.463647609000806 0.46364760900080611621
diff --git a/help/acsc b/help/acsc
index 874bfdb..dfa5d7e 100644
--- a/help/acsc
+++ b/help/acsc
@@ -14,6 +14,14 @@ DESCRIPTION
     Returns the inverse cosecant of x to a multiple of eps with error less in
     absolute value than .75 * eps.
 
+    This function is sometimes called arccsc, is such that:
+
+	csc(acsc(x)) = x
+
+    and such that:
+
+	acsc(x) = asin(1/x)
+
 EXAMPLE
     ; print acsc(2, 1e-5), acsc(2, 1e-10), acsc(2, 1e-15), acsc(2, 1e-20)
     0.5236 0.5235987756 0.523598775598299 0.52359877559829887308
diff --git a/help/asec b/help/asec
index d196094..596a43d 100644
--- a/help/asec
+++ b/help/asec
@@ -14,6 +14,14 @@ DESCRIPTION
     Returns the inverse secant of x to a multiple of eps with error less in
     absolute value than .75 * eps.
 
+    This function is sometimes called arcsec, is such that:
+
+	sec(asec(x)) = x
+
+    and such that:
+
+	asec(x) = acos(1/x)
+
 EXAMPLE
     ; print asec(2, 1e-5), asec(2, 1e-10), asec(2, 1e-15), asec(2, 1e-20)
     1.0472 1.0471975512 1.047197551196598 1.04719755119659774615
diff --git a/help/asin b/help/asin
index 7238d75..7a5a01e 100644
--- a/help/asin
+++ b/help/asin
@@ -14,7 +14,13 @@ DESCRIPTION
     Returns the inverse sine of x to a multiple of eps with error less in
     absolute value than .75 * eps.
 
-    v = asin(x) is the number in [-pi/2, pi/2] for which sin(v) = x.
+    This function is sometimes called arcsin, is such that:
+
+	sin(asin(x)) = x
+
+    and such that:
+
+	asin(x) = acsc(1/x)
 
 EXAMPLE
     ; print asin(.5, 1e-5), asin(.5, 1e-10), asin(.5, 1e-15), asin(.5, 1e-20)
diff --git a/help/atan b/help/atan
index 362227c..dc99649 100644
--- a/help/atan
+++ b/help/atan
@@ -14,6 +14,14 @@ DESCRIPTION
     Returns the inverse tangent of x to a multiple of eps with error less in
     absolute value than .75 * eps.
 
+    This function is sometimes called arctan, is such that:
+
+	tan(atan(x)) = x
+
+    and such that:
+
+	atan(x) = acot(1/x)
+
 EXAMPLE
     ; print atan(2, 1e-5), atan(2, 1e-10), atan(2, 1e-15), atan(2, 1e-20)
     1.10715 1.1071487178 1.107148717794091 1.10714871779409050302