From e8da515a6c1eb1ac45a9104b884fa093456a1b12 Mon Sep 17 00:00:00 2001
From: Karan Anand <anandkarancompsci@gmail.com>
Date: Thu, 27 Aug 2026 09:51:05 +0530
Subject: [PATCH] docs: add equations to trigonometric function READMEs

Add defining equations to the intro sections of sin, cos, cot, sec,
csc and their single-precision and degree variants.

Ref: https://github.com/stdlib-js/metr-issue-tracker/issues/1257
---
 .../@stdlib/math/base/special/cos/README.md      | 16 ++++++++++++++++
 .../@stdlib/math/base/special/cosd/README.md     | 10 ++++++++++
 .../@stdlib/math/base/special/cosdf/README.md    | 10 ++++++++++
 .../@stdlib/math/base/special/cosf/README.md     | 16 ++++++++++++++++
 .../@stdlib/math/base/special/cot/README.md      | 10 ++++++++++
 .../@stdlib/math/base/special/cotd/README.md     | 10 ++++++++++
 .../@stdlib/math/base/special/cotdf/README.md    | 10 ++++++++++
 .../@stdlib/math/base/special/cotf/README.md     | 10 ++++++++++
 .../@stdlib/math/base/special/csc/README.md      | 10 ++++++++++
 .../@stdlib/math/base/special/cscd/README.md     | 16 ++++++++++++++++
 .../@stdlib/math/base/special/cscdf/README.md    | 16 ++++++++++++++++
 .../@stdlib/math/base/special/cscf/README.md     | 10 ++++++++++
 .../@stdlib/math/base/special/sec/README.md      | 10 ++++++++++
 .../@stdlib/math/base/special/secd/README.md     | 16 ++++++++++++++++
 .../@stdlib/math/base/special/secdf/README.md    | 16 ++++++++++++++++
 .../@stdlib/math/base/special/secf/README.md     | 10 ++++++++++
 .../@stdlib/math/base/special/sin/README.md      | 16 ++++++++++++++++
 .../@stdlib/math/base/special/sind/README.md     | 10 ++++++++++
 .../@stdlib/math/base/special/sindf/README.md    | 10 ++++++++++
 .../@stdlib/math/base/special/sinf/README.md     | 16 ++++++++++++++++
 .../@stdlib/math/base/special/tand/README.md     | 10 ++++++++++
 .../@stdlib/math/base/special/tandf/README.md    | 10 ++++++++++
 22 files changed, 268 insertions(+)

diff --git a/lib/node_modules/@stdlib/math/base/special/cos/README.md b/lib/node_modules/@stdlib/math/base/special/cos/README.md
index 8ef4bb9d6cb5..3f13e2d5a865 100644
--- a/lib/node_modules/@stdlib/math/base/special/cos/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/cos/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the [cosine][cosine] of a number.
 
+<section class="intro">
+
+The [cosine][cosine] function can be expressed as the infinite series
+
+<!-- <equation class="equation" label="eq:cosine_function" align="center" raw="\cos(x) = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n)!} x^{2n} = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \cdots" alt="Cosine function Taylor series expansion"> -->
+
+```math
+\cos(x) = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n)!} x^{2n} = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \cdots
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
diff --git a/lib/node_modules/@stdlib/math/base/special/cosd/README.md b/lib/node_modules/@stdlib/math/base/special/cosd/README.md
index ec72cdfd17b2..98228ec03e69 100644
--- a/lib/node_modules/@stdlib/math/base/special/cosd/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/cosd/README.md
@@ -24,6 +24,16 @@ limitations under the License.
 
 <section class="intro">
 
+The [cosine][trigonometric-functions] of an angle measured in degrees is computed as
+
+<!-- <equation class="equation" label="eq:cosine_degrees" align="center" raw="y = \cos\left(\frac{\pi x}{180}\right)" alt="Cosine of an angle in degrees"> -->
+
+```math
+y = \cos\left(\frac{\pi x}{180}\right)
+```
+
+<!-- </equation> -->
+
 </section>
 
 <!-- /.intro -->
diff --git a/lib/node_modules/@stdlib/math/base/special/cosdf/README.md b/lib/node_modules/@stdlib/math/base/special/cosdf/README.md
index 24443041a88b..98bf710f1656 100644
--- a/lib/node_modules/@stdlib/math/base/special/cosdf/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/cosdf/README.md
@@ -24,6 +24,16 @@ limitations under the License.
 
 <section class="intro">
 
+The [cosine][trigonometric-functions] of an angle measured in degrees is computed as
+
+<!-- <equation class="equation" label="eq:cosine_degrees" align="center" raw="y = \cos\left(\frac{\pi x}{180}\right)" alt="Cosine of an angle in degrees"> -->
+
+```math
+y = \cos\left(\frac{\pi x}{180}\right)
+```
+
+<!-- </equation> -->
+
 </section>
 
 <!-- /.intro -->
diff --git a/lib/node_modules/@stdlib/math/base/special/cosf/README.md b/lib/node_modules/@stdlib/math/base/special/cosf/README.md
index 791ac0018cf6..e486ba789c3b 100644
--- a/lib/node_modules/@stdlib/math/base/special/cosf/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/cosf/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the [cosine][cosine] of a single-precision floating-point number (in radians).
 
+<section class="intro">
+
+The [cosine][cosine] function can be expressed as the infinite series
+
+<!-- <equation class="equation" label="eq:cosine_function" align="center" raw="\cos(x) = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n)!} x^{2n} = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \cdots" alt="Cosine function Taylor series expansion"> -->
+
+```math
+\cos(x) = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n)!} x^{2n} = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \cdots
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
diff --git a/lib/node_modules/@stdlib/math/base/special/cot/README.md b/lib/node_modules/@stdlib/math/base/special/cot/README.md
index 897e7df2e614..6b5af6e4e38a 100644
--- a/lib/node_modules/@stdlib/math/base/special/cot/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/cot/README.md
@@ -24,6 +24,16 @@ limitations under the License.
 
 <section class="intro">
 
+The [cotangent][trigonometric-functions] function is defined as
+
+<!-- <equation class="equation" label="eq:cotangent_function" align="center" raw="y = \cot(x) = \frac{\cos(x)}{\sin(x)}" alt="Cotangent function"> -->
+
+```math
+y = \cot(x) = \frac{\cos(x)}{\sin(x)}
+```
+
+<!-- </equation> -->
+
 </section>
 
 <!-- /.intro -->
diff --git a/lib/node_modules/@stdlib/math/base/special/cotd/README.md b/lib/node_modules/@stdlib/math/base/special/cotd/README.md
index d9dbdf44a0b7..cd6067b8bf52 100644
--- a/lib/node_modules/@stdlib/math/base/special/cotd/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/cotd/README.md
@@ -24,6 +24,16 @@ limitations under the License.
 
 <section class="intro">
 
+The [cotangent][trigonometric-functions] of an angle measured in degrees is computed as
+
+<!-- <equation class="equation" label="eq:cotangent_degrees" align="center" raw="y = \cot\left(\frac{\pi x}{180}\right)" alt="Cotangent of an angle in degrees"> -->
+
+```math
+y = \cot\left(\frac{\pi x}{180}\right)
+```
+
+<!-- </equation> -->
+
 </section>
 
 <!-- /.intro -->
diff --git a/lib/node_modules/@stdlib/math/base/special/cotdf/README.md b/lib/node_modules/@stdlib/math/base/special/cotdf/README.md
index bccb71ef5b26..ac17bc7c8485 100644
--- a/lib/node_modules/@stdlib/math/base/special/cotdf/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/cotdf/README.md
@@ -24,6 +24,16 @@ limitations under the License.
 
 <section class="intro">
 
+The [cotangent][trigonometric-functions] of an angle measured in degrees is computed as
+
+<!-- <equation class="equation" label="eq:cotangent_degrees" align="center" raw="y = \cot\left(\frac{\pi x}{180}\right)" alt="Cotangent of an angle in degrees"> -->
+
+```math
+y = \cot\left(\frac{\pi x}{180}\right)
+```
+
+<!-- </equation> -->
+
 </section>
 
 <!-- /.intro -->
diff --git a/lib/node_modules/@stdlib/math/base/special/cotf/README.md b/lib/node_modules/@stdlib/math/base/special/cotf/README.md
index b19044590e02..99dd3c2ddab1 100644
--- a/lib/node_modules/@stdlib/math/base/special/cotf/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/cotf/README.md
@@ -24,6 +24,16 @@ limitations under the License.
 
 <section class="intro">
 
+The [cotangent][trigonometric-functions] function is defined as
+
+<!-- <equation class="equation" label="eq:cotangent_function" align="center" raw="y = \cot(x) = \frac{\cos(x)}{\sin(x)}" alt="Cotangent function"> -->
+
+```math
+y = \cot(x) = \frac{\cos(x)}{\sin(x)}
+```
+
+<!-- </equation> -->
+
 </section>
 
 <!-- /.intro -->
diff --git a/lib/node_modules/@stdlib/math/base/special/csc/README.md b/lib/node_modules/@stdlib/math/base/special/csc/README.md
index 57cc03fda1ae..30bba15236bd 100644
--- a/lib/node_modules/@stdlib/math/base/special/csc/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/csc/README.md
@@ -24,6 +24,16 @@ limitations under the License.
 
 <section class="intro">
 
+The [cosecant][trigonometric-functions] function is defined as
+
+<!-- <equation class="equation" label="eq:cosecant_function" align="center" raw="y = \csc(x) = \frac{1}{\sin(x)}" alt="Cosecant function"> -->
+
+```math
+y = \csc(x) = \frac{1}{\sin(x)}
+```
+
+<!-- </equation> -->
+
 </section>
 
 <!-- /.intro -->
diff --git a/lib/node_modules/@stdlib/math/base/special/cscd/README.md b/lib/node_modules/@stdlib/math/base/special/cscd/README.md
index 7c681574a80f..5d38a741afe7 100644
--- a/lib/node_modules/@stdlib/math/base/special/cscd/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/cscd/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the [cosecant][cosecant] of a degree.
 
+<section class="intro">
+
+The [cosecant][cosecant] of an angle measured in degrees is computed as
+
+<!-- <equation class="equation" label="eq:cosecant_degrees" align="center" raw="y = \csc\left(\frac{\pi x}{180}\right)" alt="Cosecant of an angle in degrees"> -->
+
+```math
+y = \csc\left(\frac{\pi x}{180}\right)
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
diff --git a/lib/node_modules/@stdlib/math/base/special/cscdf/README.md b/lib/node_modules/@stdlib/math/base/special/cscdf/README.md
index e595d7a1b2a3..467e6bdb9895 100644
--- a/lib/node_modules/@stdlib/math/base/special/cscdf/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/cscdf/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the [cosecant][cosecant] of a single-precision floating-point number (in degrees).
 
+<section class="intro">
+
+The [cosecant][cosecant] of an angle measured in degrees is computed as
+
+<!-- <equation class="equation" label="eq:cosecant_degrees" align="center" raw="y = \csc\left(\frac{\pi x}{180}\right)" alt="Cosecant of an angle in degrees"> -->
+
+```math
+y = \csc\left(\frac{\pi x}{180}\right)
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
diff --git a/lib/node_modules/@stdlib/math/base/special/cscf/README.md b/lib/node_modules/@stdlib/math/base/special/cscf/README.md
index e65c7908d066..761f5310d58c 100644
--- a/lib/node_modules/@stdlib/math/base/special/cscf/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/cscf/README.md
@@ -24,6 +24,16 @@ limitations under the License.
 
 <section class="intro">
 
+The [cosecant][trigonometric-functions] function is defined as
+
+<!-- <equation class="equation" label="eq:cosecant_function" align="center" raw="y = \csc(x) = \frac{1}{\sin(x)}" alt="Cosecant function"> -->
+
+```math
+y = \csc(x) = \frac{1}{\sin(x)}
+```
+
+<!-- </equation> -->
+
 </section>
 
 <!-- /.intro -->
diff --git a/lib/node_modules/@stdlib/math/base/special/sec/README.md b/lib/node_modules/@stdlib/math/base/special/sec/README.md
index 8c1b685664a2..f346718b6ea7 100644
--- a/lib/node_modules/@stdlib/math/base/special/sec/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/sec/README.md
@@ -24,6 +24,16 @@ limitations under the License.
 
 <section class="intro">
 
+The [secant][trigonometric-functions] function is defined as
+
+<!-- <equation class="equation" label="eq:secant_function" align="center" raw="y = \sec(x) = \frac{1}{\cos(x)}" alt="Secant function"> -->
+
+```math
+y = \sec(x) = \frac{1}{\cos(x)}
+```
+
+<!-- </equation> -->
+
 </section>
 
 <!-- /.intro -->
diff --git a/lib/node_modules/@stdlib/math/base/special/secd/README.md b/lib/node_modules/@stdlib/math/base/special/secd/README.md
index 0e91d5f7ba1b..ae5476ae578a 100644
--- a/lib/node_modules/@stdlib/math/base/special/secd/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/secd/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the [secant][secant] of an angle measured in degrees.
 
+<section class="intro">
+
+The [secant][secant] of an angle measured in degrees is computed as
+
+<!-- <equation class="equation" label="eq:secant_degrees" align="center" raw="y = \sec\left(\frac{\pi x}{180}\right) = \frac{1}{\cos\left(\frac{\pi x}{180}\right)}" alt="Secant of an angle in degrees"> -->
+
+```math
+y = \sec\left(\frac{\pi x}{180}\right) = \frac{1}{\cos\left(\frac{\pi x}{180}\right)}
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
diff --git a/lib/node_modules/@stdlib/math/base/special/secdf/README.md b/lib/node_modules/@stdlib/math/base/special/secdf/README.md
index 39fd317147dc..9964c19c9d33 100644
--- a/lib/node_modules/@stdlib/math/base/special/secdf/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/secdf/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the [secant][secant] of a single-precision floating-point number (in degrees).
 
+<section class="intro">
+
+The [secant][secant] of an angle measured in degrees is computed as
+
+<!-- <equation class="equation" label="eq:secant_degrees" align="center" raw="y = \sec\left(\frac{\pi x}{180}\right) = \frac{1}{\cos\left(\frac{\pi x}{180}\right)}" alt="Secant of an angle in degrees"> -->
+
+```math
+y = \sec\left(\frac{\pi x}{180}\right) = \frac{1}{\cos\left(\frac{\pi x}{180}\right)}
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
diff --git a/lib/node_modules/@stdlib/math/base/special/secf/README.md b/lib/node_modules/@stdlib/math/base/special/secf/README.md
index 6897159fa6aa..0ba9cd5095ad 100644
--- a/lib/node_modules/@stdlib/math/base/special/secf/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/secf/README.md
@@ -24,6 +24,16 @@ limitations under the License.
 
 <section class="intro">
 
+The [secant][trigonometric-functions] function is defined as
+
+<!-- <equation class="equation" label="eq:secant_function" align="center" raw="y = \sec(x) = \frac{1}{\cos(x)}" alt="Secant function"> -->
+
+```math
+y = \sec(x) = \frac{1}{\cos(x)}
+```
+
+<!-- </equation> -->
+
 </section>
 
 <!-- /.intro -->
diff --git a/lib/node_modules/@stdlib/math/base/special/sin/README.md b/lib/node_modules/@stdlib/math/base/special/sin/README.md
index e11e183e38f5..fdfab93aeeeb 100644
--- a/lib/node_modules/@stdlib/math/base/special/sin/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/sin/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the [sine][sine] of a number.
 
+<section class="intro">
+
+The [sine][sine] function can be expressed as the infinite series
+
+<!-- <equation class="equation" label="eq:sine_function" align="center" raw="\sin(x) = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!} x^{2n+1} = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \cdots" alt="Sine function Taylor series expansion"> -->
+
+```math
+\sin(x) = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!} x^{2n+1} = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \cdots
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
diff --git a/lib/node_modules/@stdlib/math/base/special/sind/README.md b/lib/node_modules/@stdlib/math/base/special/sind/README.md
index 620765b023bf..83ecd54e0f10 100644
--- a/lib/node_modules/@stdlib/math/base/special/sind/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/sind/README.md
@@ -24,6 +24,16 @@ limitations under the License.
 
 <section class="intro">
 
+The [sine][trigonometric-functions] of an angle measured in degrees is computed as
+
+<!-- <equation class="equation" label="eq:sine_degrees" align="center" raw="y = \sin\left(\frac{\pi x}{180}\right)" alt="Sine of an angle in degrees"> -->
+
+```math
+y = \sin\left(\frac{\pi x}{180}\right)
+```
+
+<!-- </equation> -->
+
 </section>
 
 <!-- /.intro -->
diff --git a/lib/node_modules/@stdlib/math/base/special/sindf/README.md b/lib/node_modules/@stdlib/math/base/special/sindf/README.md
index 16f2b6f9f78a..5ee1aac3f550 100644
--- a/lib/node_modules/@stdlib/math/base/special/sindf/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/sindf/README.md
@@ -24,6 +24,16 @@ limitations under the License.
 
 <section class="intro">
 
+The [sine][trigonometric-functions] of an angle measured in degrees is computed as
+
+<!-- <equation class="equation" label="eq:sine_degrees" align="center" raw="y = \sin\left(\frac{\pi x}{180}\right)" alt="Sine of an angle in degrees"> -->
+
+```math
+y = \sin\left(\frac{\pi x}{180}\right)
+```
+
+<!-- </equation> -->
+
 </section>
 
 <!-- /.intro -->
diff --git a/lib/node_modules/@stdlib/math/base/special/sinf/README.md b/lib/node_modules/@stdlib/math/base/special/sinf/README.md
index 2d91a38efb50..cc32e912ddd1 100644
--- a/lib/node_modules/@stdlib/math/base/special/sinf/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/sinf/README.md
@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the [sine][sine] of a single-precision floating-point number (in radians).
 
+<section class="intro">
+
+The [sine][sine] function can be expressed as the infinite series
+
+<!-- <equation class="equation" label="eq:sine_function" align="center" raw="\sin(x) = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!} x^{2n+1} = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \cdots" alt="Sine function Taylor series expansion"> -->
+
+```math
+\sin(x) = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!} x^{2n+1} = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \cdots
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
diff --git a/lib/node_modules/@stdlib/math/base/special/tand/README.md b/lib/node_modules/@stdlib/math/base/special/tand/README.md
index acd0292d57ba..f768b3038c43 100644
--- a/lib/node_modules/@stdlib/math/base/special/tand/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/tand/README.md
@@ -24,6 +24,16 @@ limitations under the License.
 
 <section class="intro">
 
+The [tangent][trigonometric-functions] of an angle measured in degrees is computed as
+
+<!-- <equation class="equation" label="eq:tangent_degrees" align="center" raw="y = \tan\left(\frac{\pi x}{180}\right)" alt="Tangent of an angle in degrees"> -->
+
+```math
+y = \tan\left(\frac{\pi x}{180}\right)
+```
+
+<!-- </equation> -->
+
 </section>
 
 <!-- /.intro -->
diff --git a/lib/node_modules/@stdlib/math/base/special/tandf/README.md b/lib/node_modules/@stdlib/math/base/special/tandf/README.md
index edfbfa62d267..33ecd4ead5f5 100644
--- a/lib/node_modules/@stdlib/math/base/special/tandf/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/tandf/README.md
@@ -24,6 +24,16 @@ limitations under the License.
 
 <section class="intro">
 
+The [tangent][trigonometric-functions] of an angle measured in degrees is computed as
+
+<!-- <equation class="equation" label="eq:tangent_degrees" align="center" raw="y = \tan\left(\frac{\pi x}{180}\right)" alt="Tangent of an angle in degrees"> -->
+
+```math
+y = \tan\left(\frac{\pi x}{180}\right)
+```
+
+<!-- </equation> -->
+
 </section>
 
 <!-- /.intro -->