Arcvercosine

Compute the inverse versed cosine.

The inverse versed cosine is defined as

$$\mathop{\mathrm{avercos}}(\theta) = \arccos(1+\theta)$$

Usage

var avercos = require( '@stdlib/math/base/special/avercos' );

avercos( x )

Computes the inverse versed cosine.

var v = avercos( 0.0 );
// returns 0.0

v = avercos( -3.141592653589793/2.0 );
// returns ~2.1783

v = avercos( -3.141592653589793/6.0 );
// returns ~1.0742

If x < -2, x > 0, or x is NaN, the function returns NaN.

var v = avercos( 1.0 );
// returns NaN

v = avercos( -3.14 );
// returns NaN

v = avercos( NaN );
// returns NaN

Examples

var uniform = require( '@stdlib/random/array/uniform' );
var logEachMap = require( '@stdlib/console/log-each-map' );
var avercos = require( '@stdlib/math/base/special/avercos' );

var x = uniform( 100, -2.0, 0.0, {
    'dtype': 'float64'
});

logEachMap( 'avercos(%0.4f) = %0.4f', x, avercos );

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C APIs

Usage

#include "stdlib/math/base/special/avercos.h"

stdlib_base_avercos( x )

Computes the inverse versed cosine of a double-precision floating-point number (in radians).

double out = stdlib_base_avercos( -3.141592653589793/2.0 );
// returns ~2.1783

If x < -2, x > 0, or x is NaN, the function returns NaN.

double out = stdlib_base_avercos( -3.141592653589793 );
// returns NaN

The function accepts the following arguments:

• x: [in] double input value.

double stdlib_base_avercos( const double x );

Examples

#include "stdlib/math/base/special/avercos.h"
#include <stdio.h>

int main( void ) {
    const double x[] = { -2.5, -2.0, -1.5, -1.0, -0.5, 0.5, 1.0, 1.5, 2.0, 2.5 };

    double v;
    int i;
    for ( i = 0; i < 10; i++ ) {
        v = stdlib_base_avercos( x[ i ] );
        printf( "avercos(%lf) = %lf\n", x[ i ], v );
    }
}

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See Also

• @stdlib/math/base/special/aversin: compute the inverse versed sine.
• @stdlib/math/base/special/versin: compute the versed sine.