docs: add equations

lib/node_modules/@stdlib/math/base/special/atan2/README.md

@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the angle in the plane (in radians) between the positive x-axis and the ray from `(0,0)` to the point `(x,y)`.
 
+<section class="intro">
+
+The two-argument [arctangent][arctangent] function is defined as
+
+<!-- <equation class="equation" label="eq:atan2_function" align="center" raw="\operatorname{atan2}(y, x) = \begin{cases} \arctan\!\left(\tfrac{y}{x}\right) & \textrm{if}\ x > 0 \\ \arctan\!\left(\tfrac{y}{x}\right) + \pi & \textrm{if}\ x < 0,\ y \geq 0 \\ \arctan\!\left(\tfrac{y}{x}\right) - \pi & \textrm{if}\ x < 0,\ y < 0 \\ +\tfrac{\pi}{2} & \textrm{if}\ x = 0,\ y > 0 \\ -\tfrac{\pi}{2} & \textrm{if}\ x = 0,\ y < 0 \end{cases}" alt="Two-argument arctangent function"> -->
+
+```math
+\mathop{\mathrm{atan2}}(y, x) = \begin{cases} \arctan\!\left(\tfrac{y}{x}\right) & \textrm{if}\ x > 0 \\ \arctan\!\left(\tfrac{y}{x}\right) + \pi & \textrm{if}\ x < 0,\ y \geq 0 \\ \arctan\!\left(\tfrac{y}{x}\right) - \pi & \textrm{if}\ x < 0,\ y < 0 \\ +\tfrac{\pi}{2} & \textrm{if}\ x = 0,\ y > 0 \\ -\tfrac{\pi}{2} & \textrm{if}\ x = 0,\ y < 0 \end{cases}
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
@@ -35,19 +51,19 @@ var atan2 = require( '@stdlib/math/base/special/atan2' );
 Computes the angle in the plane (in radians) between the positive x-axis and the ray from `(0,0)` to the point `(x,y)`.
 
 ```javascript
-var v = atan2( 2.0, 2.0 ); // => atan(1.0)
+var v = atan2( 2.0, 2.0 );
 // returns ~0.785
 
-v = atan2( 6.0, 2.0 ); // => atan(3.0)
+v = atan2( 6.0, 2.0 );
 // returns ~1.249
 
-v = atan2( -1.0, -1.0 ); // => atan(1.0) - π
+v = atan2( -1.0, -1.0 );
 // returns ~-2.356
 
-v = atan2( 3.0, 0.0 ); // => π/2
+v = atan2( 3.0, 0.0 );
 // returns ~1.571
 
-v = atan2( -2.0, 0.0 ); // => -π/2
+v = atan2( -2.0, 0.0 );
 // returns ~-1.571
 
 v = atan2( 0.0, 0.0 );
@@ -197,6 +213,8 @@ int main( void ) {
 
 <section class="links">
 
+[arctangent]: https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+
 <!-- <related-links> -->
 
 [@stdlib/math/base/special/atan]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/atan

lib/node_modules/@stdlib/math/base/special/atan2d/README.md

@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the angle in the plane (in degrees) between the positive x-axis and the ray from `(0,0)` to the point `(x,y)`.
 
+<section class="intro">
+
+The two-argument [arctangent][arctangent] function returning an angle in degrees is defined as
+
+<!-- <equation class="equation" label="eq:atan2d_function" align="center" raw="\operatorname{atan2d}(y, x) = \frac{180}{\pi} \operatorname{atan2}(y, x) = \begin{cases} \frac{180}{\pi}\arctan\!\left(\tfrac{y}{x}\right) & \textrm{if}\ x > 0 \\ \frac{180}{\pi}\arctan\!\left(\tfrac{y}{x}\right) + 180 & \textrm{if}\ x < 0,\ y \geq 0 \\ \frac{180}{\pi}\arctan\!\left(\tfrac{y}{x}\right) - 180 & \textrm{if}\ x < 0,\ y < 0 \\ +90 & \textrm{if}\ x = 0,\ y > 0 \\ -90 & \textrm{if}\ x = 0,\ y < 0 \end{cases}" alt="Two-argument arctangent function in degrees"> -->
+
+```math
+\mathop{\mathrm{atan2d}}(y, x) = \frac{180}{\pi}\mathop{\mathrm{atan2}}(y, x) = \begin{cases} \frac{180}{\pi}\arctan\!\left(\tfrac{y}{x}\right) & \textrm{if}\ x > 0 \\ \frac{180}{\pi}\arctan\!\left(\tfrac{y}{x}\right) + 180 & \textrm{if}\ x < 0,\ y \geq 0 \\ \frac{180}{\pi}\arctan\!\left(\tfrac{y}{x}\right) - 180 & \textrm{if}\ x < 0,\ y < 0 \\ +90 & \textrm{if}\ x = 0,\ y > 0 \\ -90 & \textrm{if}\ x = 0,\ y < 0 \end{cases}
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
@@ -35,13 +51,13 @@ var atan2d = require( '@stdlib/math/base/special/atan2d' );
 Computes the angle in the plane (in degrees) between the positive x-axis and the ray from `(0,0)` to the point `(x,y)`.
 
 ```javascript
-var v = atan2d( 2.0, 2.0 ); // => atand(1.0)
+var v = atan2d( 2.0, 2.0 );
 // returns ~45.0
 
-v = atan2d( 6.0, 2.0 ); // => atand(3.0)
+v = atan2d( 6.0, 2.0 );
 // returns ~71.565
 
-v = atan2d( -1.0, -1.0 ); // => atand(1.0) - 180.0
+v = atan2d( -1.0, -1.0 );
 // returns ~-135.0
 
 v = atan2d( 3.0, 0.0 );
@@ -192,6 +208,8 @@ int main( void ) {
 
 <section class="links">
 
+[arctangent]: https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+
 <!-- <related-links> -->
 
 <!-- </related-links> -->

lib/node_modules/@stdlib/math/base/special/atan2f/README.md

@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the angle in the plane (in radians) between the positive x-axis and the ray from `(0,0)` to the point `(x,y)` as a single-precision floating-point number.
 
+<section class="intro">
+
+The two-argument [arctangent][arctangent] function is defined as
+
+<!-- <equation class="equation" label="eq:atan2_function" align="center" raw="\operatorname{atan2}(y, x) = \begin{cases} \arctan\!\left(\tfrac{y}{x}\right) & \textrm{if}\ x > 0 \\ \arctan\!\left(\tfrac{y}{x}\right) + \pi & \textrm{if}\ x < 0,\ y \geq 0 \\ \arctan\!\left(\tfrac{y}{x}\right) - \pi & \textrm{if}\ x < 0,\ y < 0 \\ +\tfrac{\pi}{2} & \textrm{if}\ x = 0,\ y > 0 \\ -\tfrac{\pi}{2} & \textrm{if}\ x = 0,\ y < 0 \end{cases}" alt="Two-argument arctangent function"> -->
+
+```math
+\mathop{\mathrm{atan2}}(y, x) = \begin{cases} \arctan\!\left(\tfrac{y}{x}\right) & \textrm{if}\ x > 0 \\ \arctan\!\left(\tfrac{y}{x}\right) + \pi & \textrm{if}\ x < 0,\ y \geq 0 \\ \arctan\!\left(\tfrac{y}{x}\right) - \pi & \textrm{if}\ x < 0,\ y < 0 \\ +\tfrac{\pi}{2} & \textrm{if}\ x = 0,\ y > 0 \\ -\tfrac{\pi}{2} & \textrm{if}\ x = 0,\ y < 0 \end{cases}
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
@@ -35,19 +51,19 @@ var atan2f = require( '@stdlib/math/base/special/atan2f' );
 Computes the angle in the plane (in radians) between the positive x-axis and the ray from `(0,0)` to the point `(x,y)` as a single-precision floating-point number.
 
 ```javascript
-var v = atan2f( 2.0, 2.0 ); // => atanf( 1.0 )
+var v = atan2f( 2.0, 2.0 );
 // returns ~0.785
 
-v = atan2f( 6.0, 2.0 ); // => atanf( 3.0 )
+v = atan2f( 6.0, 2.0 );
 // returns ~1.249
 
-v = atan2f( -1.0, -1.0 ); // => atanf( 1.0 ) - π
+v = atan2f( -1.0, -1.0 );
 // returns ~-2.356
 
-v = atan2f( 3.0, 0.0 ); // => π/2
+v = atan2f( 3.0, 0.0 );
 // returns ~1.571
 
-v = atan2f( -2.0, 0.0 ); // => -π/2
+v = atan2f( -2.0, 0.0 );
 // returns ~-1.571
 
 v = atan2f( 0.0, 0.0 );
@@ -191,6 +207,8 @@ int main( void ) {
 
 <section class="links">
 
+[arctangent]: https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+
 <!-- <related-links> -->
 
 <!-- </related-links> -->

lib/node_modules/@stdlib/math/base/special/cosm1/README.md

@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute `cos(x) - 1`.
 
+<section class="intro">
+
+The function computes `cos(x) - 1` accurately for small `x`
+
+<!-- <equation class="equation" label="eq:cosm1_function" align="center" raw="y = \cos(x) - 1" alt="Cosine minus one"> -->
+
+```math
+y = \cos(x) - 1
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage

lib/node_modules/@stdlib/math/base/special/cosm1f/README.md

@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute `cos(x) - 1`.
 
+<section class="intro">
+
+The function computes `cos(x) - 1` accurately for small `x`
+
+<!-- <equation class="equation" label="eq:cosm1_function" align="center" raw="y = \cos(x) - 1" alt="Cosine minus one"> -->
+
+```math
+y = \cos(x) - 1
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage

lib/node_modules/@stdlib/math/base/special/cospi/README.md

@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the [cosine][@stdlib/math/base/special/cos] of a number times [π][@stdlib/constants/float64/pi].
 
+<section class="intro">
+
+The function computes the [cosine][cosine] of a number scaled by `π`
+
+<!-- <equation class="equation" label="eq:cospi_function" align="center" raw="y = \cos(\pi x)" alt="Cosine of pi times x"> -->
+
+```math
+y = \cos(\pi x)
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
@@ -178,6 +194,8 @@ int main( void ) {
 
 <section class="links">
 
+[cosine]: https://en.wikipedia.org/wiki/Cosine
+
 [@stdlib/constants/float64/pi]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/constants/float64/pi
 
 <!-- <related-links> -->

lib/node_modules/@stdlib/math/base/special/cospif/README.md

@@ -22,6 +22,22 @@ limitations under the License.
 
 > Compute the [cosine][@stdlib/math/base/special/cosf] of a number times [π][@stdlib/constants/float32/pi].
 
+<section class="intro">
+
+The function computes the [cosine][cosine] of a number scaled by `π`
+
+<!-- <equation class="equation" label="eq:cospi_function" align="center" raw="y = \cos(\pi x)" alt="Cosine of pi times x"> -->
+
+```math
+y = \cos(\pi x)
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
@@ -172,6 +188,8 @@ int main( void ) {
 
 <section class="links">
 
+[cosine]: https://en.wikipedia.org/wiki/Cosine
+
 [@stdlib/constants/float32/pi]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/constants/float32/pi
 
 [@stdlib/math/base/special/cosf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/cosf

lib/node_modules/@stdlib/math/base/special/sincos/README.md

@@ -22,6 +22,22 @@ limitations under the License.
 
 > Simultaneously compute the [sine][@stdlib/math/base/special/sin] and [cosine][@stdlib/math/base/special/cos] of an angle measured in radians.
 
+<section class="intro">
+
+The function simultaneously computes the [sine][sine] and [cosine][cosine] of a number
+
+<!-- <equation class="equation" label="eq:sincos_function" align="center" raw="(y_s, y_c) = (\sin(x),\; \cos(x))" alt="Simultaneous sine and cosine"> -->
+
+```math
+(y_s, y_c) = (\sin(x),\; \cos(x))
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
@@ -198,6 +214,10 @@ int main( void ) {
 
 <section class="links">
 
+[cosine]: https://en.wikipedia.org/wiki/Cosine
+
+[sine]: https://en.wikipedia.org/wiki/Sine
+
 <!-- <related-links> -->
 
 [@stdlib/math/base/special/cos]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/cos

lib/node_modules/@stdlib/math/base/special/sincosd/README.md

@@ -22,6 +22,22 @@ limitations under the License.
 
 > Simultaneously compute the [sine][@stdlib/math/base/special/sind] and [cosine][@stdlib/math/base/special/cosd] of an angle measured in degrees.
 
+<section class="intro">
+
+The function simultaneously computes the [sine][trigonometric-functions] and [cosine][trigonometric-functions] of an angle measured in degrees
+
+<!-- <equation class="equation" label="eq:sincosd_function" align="center" raw="(y_s, y_c) = \left(\sin\!\left(\frac{\pi x}{180}\right),\; \cos\!\left(\frac{\pi x}{180}\right)\right)" alt="Simultaneous sine and cosine of an angle in degrees"> -->
+
+```math
+(y_s, y_c) = \left(\sin\!\left(\frac{\pi x}{180}\right),\; \cos\!\left(\frac{\pi x}{180}\right)\right)
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
@@ -191,6 +207,8 @@ int main( void ) {
 
 <section class="links">
 
+[trigonometric-functions]: https://en.wikipedia.org/wiki/Trigonometric_functions
+
 [@stdlib/math/base/special/cosd]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/cosd
 
 [@stdlib/math/base/special/sind]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/sind

lib/node_modules/@stdlib/math/base/special/sincosdf/README.md

@@ -22,6 +22,22 @@ limitations under the License.
 
 > Simultaneously compute the [sine][@stdlib/math/base/special/sindf] and [cosine][@stdlib/math/base/special/cosdf] of a single-precision floating-point number (in degrees).
 
+<section class="intro">
+
+The function simultaneously computes the [sine][trigonometric-functions] and [cosine][trigonometric-functions] of an angle measured in degrees
+
+<!-- <equation class="equation" label="eq:sincosd_function" align="center" raw="(y_s, y_c) = \left(\sin\!\left(\frac{\pi x}{180}\right),\; \cos\!\left(\frac{\pi x}{180}\right)\right)" alt="Simultaneous sine and cosine of an angle in degrees"> -->
+
+```math
+(y_s, y_c) = \left(\sin\!\left(\frac{\pi x}{180}\right),\; \cos\!\left(\frac{\pi x}{180}\right)\right)
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
 <section class="usage">
 
 ## Usage
@@ -191,6 +207,8 @@ int main( void ) {
 
 <section class="links">
 
+[trigonometric-functions]: https://en.wikipedia.org/wiki/Trigonometric_functions
+
 [@stdlib/math/base/special/cosdf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/cosdf
 
 [@stdlib/math/base/special/sindf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/sindf