npm package: @stdlib/math-base-special-hacoversin
Description: Compute the half-value coversed sine.
Author: The Stdlib Authors
Latest version: 0.3.1

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# Hacoversine

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Compute the half-value [coversed sine][coversed-sine].

<section class="intro">

The half-value [coversed sine][coversed-sine] is defined as

<!-- <equation class="equation" label="eq:hacoversine" align="center" raw="\operatorname{hacoversin}(\theta) = \frac{1 - \sin \theta}{2}" alt="Half-value coversed sine."> -->

<div class="equation" align="center" data-raw-text="\operatorname{hacoversin}(\theta) = \frac{1 - \sin \theta}{2}" data-equation="eq:hacoversine">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/hacoversin/docs/img/equation_hacoversine.svg" alt="Half-value coversed sine.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/math-base-special-hacoversin
```

</section>

<section class="usage">

## Usage

```javascript
var hacoversin = require( '@stdlib/math-base-special-hacoversin' );
```

#### hacoversin( x )

Computes the half-value [coversed sine][coversed-sine] (in radians).

```javascript
var v = hacoversin( 0.0 );
// returns 0.5

v = hacoversin( 3.141592653589793/2.0 );
// returns 0.0

v = hacoversin( -3.141592653589793/6.0 );
// returns 0.75
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var TWO_PI = require( '@stdlib/constants-float64-two-pi' );
var hacoversin = require( '@stdlib/math-base-special-hacoversin' );

var opts = {
    'dtype': 'float64'
};
var x = uniform( 100, 0.0, TWO_PI, opts );

logEachMap( 'hacoversin(%0.4f) = %0.4f', x, hacoversin );
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/math/base/special/hacoversin.h"
```

#### stdlib_base_hacoversin( x )

Computes the half-value [coversed sine][coversed-sine] (in radians).

```c
double out = stdlib_base_hacoversin( 0.0 );
// returns 0.5

out = stdlib_base_hacoversin( 3.141592653589793 / 2.0 );
// returns 0.0
```

The function accepts the following arguments:

-   **x**: `[in] double` input value.

```c
double stdlib_base_hacoversin( const double x );
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/math/base/special/hacoversin.h"
#include <stdio.h>

int main( void ) {
    const double x[] = { 0.0, 0.523, 0.785, 1.047, 3.14 };

    double y;
    int i;
    for ( i = 0; i < 5; i++ ) {
        y = stdlib_base_hacoversin( x[ i ] );
        printf( "hacoversin(%lf) = %lf\n", x[ i ], y );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/math-base/special/hacovercos`][@stdlib/math/base/special/hacovercos]</span><span class="delimiter">: </span><span class="description">compute the half-value coversed cosine.</span>
-   <span class="package-name">[`@stdlib/math-base/special/haversin`][@stdlib/math/base/special/haversin]</span><span class="delimiter">: </span><span class="description">compute the half-value versed sine.</span>

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

#### Community

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-special-hacoversin/main/LICENSE

[coversed-sine]: https://en.wikipedia.org/wiki/Versine

<!-- <related-links> -->

[@stdlib/math/base/special/hacovercos]: https://www.npmjs.com/package/@stdlib/math-base-special-hacovercos

[@stdlib/math/base/special/haversin]: https://www.npmjs.com/package/@stdlib/math-base-special-haversin

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</section>

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