# NAG Library Routine Document

## 1Purpose

f06bcf reconstructs the parameters $c$ and $s$ of a real plane rotation from the tangent of that rotation.

## 2Specification

Fortran Interface
 Subroutine f06bcf ( t, c, s)
 Real (Kind=nag_wp), Intent (In) :: t Real (Kind=nag_wp), Intent (Out) :: c, s
C Header Interface
#include nagmk26.h
 void f06bcf_ (const double *t, double *c, double *s)

## 3Description

f06bcf reconstructs the parameters $c$ and $s$ of a real plane rotation from the value of the tangent $t$, as returned by f06baf:
 $c=11+t2 , s=ct,$
so that $c\ge 0$ and $s$ has the same sign as $t$.
If $\left|t\right|<\sqrt{\epsilon }$, where $\epsilon$ is the machine precision, the routine sets $c=1$ and $s=t$; if $\left|t\right|>1/\sqrt{\epsilon }$, the routine sets $c=\frac{1}{\left|t\right|}$ and $s=\mathrm{sign}t$.

None.

## 5Arguments

1:     $\mathbf{t}$ – Real (Kind=nag_wp)Input
On entry: the value $t$, the tangent of the rotation.
2:     $\mathbf{c}$ – Real (Kind=nag_wp)Output
On exit: the value $c$, the cosine of the rotation.
3:     $\mathbf{s}$ – Real (Kind=nag_wp)Output
On exit: the value $s$, the sine of the rotation.

None.

Not applicable.

## 8Parallelism and Performance

f06bcf is not threaded in any implementation.

None.

## 10Example

None.
© The Numerical Algorithms Group Ltd, Oxford, UK. 2017