diff --git a/lib/node_modules/@stdlib/math/base/special/atan2/README.md b/lib/node_modules/@stdlib/math/base/special/atan2/README.md
index ae83ba4074a4..272391c18784 100755
--- a/lib/node_modules/@stdlib/math/base/special/atan2/README.md
+++ b/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)`.
+
+
+The two-argument [arctangent][arctangent] function is defined as
+
+
+
+```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}
+```
+
+
+
+
+
+
+
## 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 ) {
+[arctangent]: https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+
[@stdlib/math/base/special/atan]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/atan
diff --git a/lib/node_modules/@stdlib/math/base/special/atan2d/README.md b/lib/node_modules/@stdlib/math/base/special/atan2d/README.md
index fec877abb79d..3aae8b5b5cd4 100755
--- a/lib/node_modules/@stdlib/math/base/special/atan2d/README.md
+++ b/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)`.
+
+
+The two-argument [arctangent][arctangent] function returning an angle in degrees is defined as
+
+
+
+```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}
+```
+
+
+
+
+
+
+
## 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 ) {
+[arctangent]: https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+
diff --git a/lib/node_modules/@stdlib/math/base/special/atan2f/README.md b/lib/node_modules/@stdlib/math/base/special/atan2f/README.md
index 7285ee42a6f8..8593ee3545b7 100755
--- a/lib/node_modules/@stdlib/math/base/special/atan2f/README.md
+++ b/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.
+
+
+The two-argument [arctangent][arctangent] function is defined as
+
+
+
+```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}
+```
+
+
+
+
+
+
+
## 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 ) {
+[arctangent]: https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+
diff --git a/lib/node_modules/@stdlib/math/base/special/cosm1/README.md b/lib/node_modules/@stdlib/math/base/special/cosm1/README.md
index 200f79b7ad85..def42b411c91 100644
--- a/lib/node_modules/@stdlib/math/base/special/cosm1/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/cosm1/README.md
@@ -22,6 +22,22 @@ limitations under the License.
> Compute `cos(x) - 1`.
+
+
+The function computes `cos(x) - 1` accurately for small `x`
+
+
+
+```math
+y = \cos(x) - 1
+```
+
+
+
+
+
+
+
## Usage
diff --git a/lib/node_modules/@stdlib/math/base/special/cosm1f/README.md b/lib/node_modules/@stdlib/math/base/special/cosm1f/README.md
index 3a4ed265f183..cd389f636c1c 100644
--- a/lib/node_modules/@stdlib/math/base/special/cosm1f/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/cosm1f/README.md
@@ -22,6 +22,22 @@ limitations under the License.
> Compute `cos(x) - 1`.
+
+
+The function computes `cos(x) - 1` accurately for small `x`
+
+
+
+```math
+y = \cos(x) - 1
+```
+
+
+
+
+
+
+
## Usage
diff --git a/lib/node_modules/@stdlib/math/base/special/cospi/README.md b/lib/node_modules/@stdlib/math/base/special/cospi/README.md
index 45e09dd1aa80..fc242db8d35a 100644
--- a/lib/node_modules/@stdlib/math/base/special/cospi/README.md
+++ b/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].
+
+
+The function computes the [cosine][cosine] of a number scaled by `π`
+
+
+
+```math
+y = \cos(\pi x)
+```
+
+
+
+
+
+
+
## Usage
@@ -178,6 +194,8 @@ int main( void ) {
+[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
diff --git a/lib/node_modules/@stdlib/math/base/special/cospif/README.md b/lib/node_modules/@stdlib/math/base/special/cospif/README.md
index fabd3e9d5434..60928ae8b6ab 100644
--- a/lib/node_modules/@stdlib/math/base/special/cospif/README.md
+++ b/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].
+
+
+The function computes the [cosine][cosine] of a number scaled by `π`
+
+
+
+```math
+y = \cos(\pi x)
+```
+
+
+
+
+
+
+
## Usage
@@ -172,6 +188,8 @@ int main( void ) {
+[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
diff --git a/lib/node_modules/@stdlib/math/base/special/sincos/README.md b/lib/node_modules/@stdlib/math/base/special/sincos/README.md
index cea6faf3a09e..6a7b5a1b89f9 100644
--- a/lib/node_modules/@stdlib/math/base/special/sincos/README.md
+++ b/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.
+
+
+The function simultaneously computes the [sine][sine] and [cosine][cosine] of a number
+
+
+
+```math
+(y_s, y_c) = (\sin(x),\; \cos(x))
+```
+
+
+
+
+
+
+
## Usage
@@ -198,6 +214,10 @@ int main( void ) {
+[cosine]: https://en.wikipedia.org/wiki/Cosine
+
+[sine]: https://en.wikipedia.org/wiki/Sine
+
[@stdlib/math/base/special/cos]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/cos
diff --git a/lib/node_modules/@stdlib/math/base/special/sincosd/README.md b/lib/node_modules/@stdlib/math/base/special/sincosd/README.md
index 276fdf307c16..3d4364188981 100644
--- a/lib/node_modules/@stdlib/math/base/special/sincosd/README.md
+++ b/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.
+
+
+The function simultaneously computes the [sine][trigonometric-functions] and [cosine][trigonometric-functions] of an angle measured in degrees
+
+
+
+```math
+(y_s, y_c) = \left(\sin\!\left(\frac{\pi x}{180}\right),\; \cos\!\left(\frac{\pi x}{180}\right)\right)
+```
+
+
+
+
+
+
+
## Usage
@@ -191,6 +207,8 @@ int main( void ) {
+[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
diff --git a/lib/node_modules/@stdlib/math/base/special/sincosdf/README.md b/lib/node_modules/@stdlib/math/base/special/sincosdf/README.md
index d4b46c2a8ba7..c03db37c19be 100644
--- a/lib/node_modules/@stdlib/math/base/special/sincosdf/README.md
+++ b/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).
+
+
+The function simultaneously computes the [sine][trigonometric-functions] and [cosine][trigonometric-functions] of an angle measured in degrees
+
+
+
+```math
+(y_s, y_c) = \left(\sin\!\left(\frac{\pi x}{180}\right),\; \cos\!\left(\frac{\pi x}{180}\right)\right)
+```
+
+
+
+
+
+
+
## Usage
@@ -191,6 +207,8 @@ int main( void ) {
+[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
diff --git a/lib/node_modules/@stdlib/math/base/special/sincosf/README.md b/lib/node_modules/@stdlib/math/base/special/sincosf/README.md
index 679924d9dec2..72c2f5394a73 100644
--- a/lib/node_modules/@stdlib/math/base/special/sincosf/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/sincosf/README.md
@@ -22,6 +22,22 @@ limitations under the License.
> Simultaneously compute the [sine][@stdlib/math/base/special/sinf] and [cosine][@stdlib/math/base/special/cosf] of a single-precision floating-point number (in radians).
+
+
+The function simultaneously computes the [sine][sine] and [cosine][cosine] of a number
+
+
+
+```math
+(y_s, y_c) = (\sin(x),\; \cos(x))
+```
+
+
+
+
+
+
+
## Usage
@@ -195,6 +211,10 @@ int main( void ) {
+[cosine]: https://en.wikipedia.org/wiki/Cosine
+
+[sine]: https://en.wikipedia.org/wiki/Sine
+
[@stdlib/math/base/special/cosf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/cosf
[@stdlib/math/base/special/sinf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/sinf
diff --git a/lib/node_modules/@stdlib/math/base/special/sincospi/README.md b/lib/node_modules/@stdlib/math/base/special/sincospi/README.md
index 06adafc353f9..8bc8676c31c2 100644
--- a/lib/node_modules/@stdlib/math/base/special/sincospi/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/sincospi/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 a number times [π][@stdlib/constants/float64/pi].
+
+
+The function simultaneously computes the [sine][sine] and [cosine][cosine] of a number scaled by `π`
+
+
+
+```math
+(y_s, y_c) = (\sin(\pi x),\; \cos(\pi x))
+```
+
+
+
+
+
+
+
## Usage
@@ -200,6 +216,10 @@ int main( void ) {
+[cosine]: https://en.wikipedia.org/wiki/Cosine
+
+[sine]: https://en.wikipedia.org/wiki/Sine
+
[@stdlib/math/base/special/sin]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/sin
[@stdlib/math/base/special/cos]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/cos
diff --git a/lib/node_modules/@stdlib/math/base/special/sincospif/README.md b/lib/node_modules/@stdlib/math/base/special/sincospif/README.md
index e67b2a4f836c..f859afd8c78c 100644
--- a/lib/node_modules/@stdlib/math/base/special/sincospif/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/sincospif/README.md
@@ -22,6 +22,22 @@ limitations under the License.
> Simultaneously compute the [sine][@stdlib/math/base/special/sinf] and [cosine][@stdlib/math/base/special/cosf] of a single-precision floating-point number times [π][@stdlib/constants/float32/pi].
+
+
+The function simultaneously computes the [sine][sine] and [cosine][cosine] of a number scaled by `π`
+
+
+
+```math
+(y_s, y_c) = (\sin(\pi x),\; \cos(\pi x))
+```
+
+
+
+
+
+
+
## Usage
@@ -202,6 +218,10 @@ int main( void ) {
+[cosine]: https://en.wikipedia.org/wiki/Cosine
+
+[sine]: https://en.wikipedia.org/wiki/Sine
+
[@stdlib/math/base/special/sinf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/sinf
[@stdlib/math/base/special/cosf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/cosf
diff --git a/lib/node_modules/@stdlib/math/base/special/sinpi/README.md b/lib/node_modules/@stdlib/math/base/special/sinpi/README.md
index b94fa78f78ce..5344b75b52de 100644
--- a/lib/node_modules/@stdlib/math/base/special/sinpi/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/sinpi/README.md
@@ -22,6 +22,22 @@ limitations under the License.
> Compute the [sine][@stdlib/math/base/special/sin] of a number times [π][@stdlib/constants/float64/pi].
+
+
+The function computes the [sine][sine] of a number scaled by `π`
+
+
+
+```math
+y = \sin(\pi x)
+```
+
+
+
+
+
+
+
## Usage
@@ -178,6 +194,8 @@ int main( void ) {
+[sine]: https://en.wikipedia.org/wiki/Sine
+
[@stdlib/constants/float64/pi]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/constants/float64/pi
diff --git a/lib/node_modules/@stdlib/math/base/special/sinpif/README.md b/lib/node_modules/@stdlib/math/base/special/sinpif/README.md
index 2621ef1a6635..65f05bccb74c 100644
--- a/lib/node_modules/@stdlib/math/base/special/sinpif/README.md
+++ b/lib/node_modules/@stdlib/math/base/special/sinpif/README.md
@@ -22,6 +22,22 @@ limitations under the License.
> Compute the [sine][@stdlib/math/base/special/sinf] of a number times [π][@stdlib/constants/float32/pi].
+
+
+The function computes the [sine][sine] of a number scaled by `π`
+
+
+
+```math
+y = \sin(\pi x)
+```
+
+
+
+
+
+
+
## Usage
@@ -172,6 +188,8 @@ int main( void ) {
+[sine]: https://en.wikipedia.org/wiki/Sine
+
[@stdlib/math/base/special/sinf]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/sinf
[@stdlib/constants/float32/pi]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/constants/float32/pi