Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]

Groups > comp.lang.c > #382904

Re: Radians Or Degrees?

From Ben Bacarisse <ben.usenet@bsb.me.uk>
Newsgroups comp.lang.c
Subject Re: Radians Or Degrees?
Date 2024-02-22 14:28 +0000
Organization A noiseless patient Spider
Message-ID <87plwobmjm.fsf@bsb.me.uk> (permalink)
References <ur5trn$3d64t$1@dont-email.me> <ur605r$3fe50$1@i2pn2.org> <ur69i3$3ftgj$2@dont-email.me>

Show all headers | View raw

Lawrence D'Oliveiro <ldo@nz.invalid> writes:

> On Thu, 22 Feb 2024 00:15:47 +0100, fir wrote:
>
>> if someone knows the reason why "6.28" radians are expected to better
>> than "1.0" 'circkles' in both mathemathics and assembly tell me - as i
>> dont know the reason
>
> It’s because trig calculations are most naturally done in radians. E.g. 
> the approximation
>
>     sin x ≅ tan x ≅ x as x → 0
>
> works only if x is in radians.

No, that applies to lots of angle measures.  Radians are the natural
angle measure because we want sin' x = cos x and cos' x = -sin x.  sin
and cos are the unique solution to that pair of differential equations
(with initial conditions sin 0 = 0 and cos 0 = 1).

> Also the Euler identity
>
>      ix
>     e   = cos x + i sin x
>
> only holds if x is in radians. And so on and so on.

Yes, and there's another nod to the calculus here because just as sin an
cos are (with a minus sign) derivatives of each other, e^x is the
derivative of itself.

-- 
Ben.

Back to comp.lang.c | Previous | Next — Previous in thread | Next in thread | Find similar | Unroll thread

Thread

Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-21 22:35 +0000
  Re: Radians Or Degrees? James Kuyper <jameskuyper@alumni.caltech.edu> - 2024-02-21 17:55 -0500
    Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-02-22 01:59 +0200
      Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 01:55 +0000
        Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-22 19:14 +0000
          Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 19:48 +0000
            Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-22 20:16 +0000
              Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 21:04 +0000
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-02-22 23:39 +0200
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 21:47 +0000
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-02-22 22:57 +0000
                Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-23 00:13 +0000
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-22 16:49 -0800
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-22 16:59 -0800
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-02-23 02:42 +0000
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-23 12:28 -0800
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-23 22:42 +0000
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-24 12:40 -0800
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-24 22:52 +0000
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-24 19:26 -0800
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-25 06:30 +0000
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-22 21:58 -0700
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-02-23 02:28 +0000
                Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-02-23 11:10 +0100
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-14 11:26 +0200
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-14 17:34 +0000
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-14 19:48 +0000
                Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-03-15 12:16 +0100
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-03-14 20:30 +0000
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-14 15:12 -0700
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-14 22:19 +0000
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-14 15:21 -0700
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-14 15:22 -0700
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-15 13:49 +0200
                Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-03-15 11:23 +0100
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-15 14:15 +0200
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-16 01:23 +0000
                Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-03-16 16:59 +0100
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-15 13:59 -0700
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-15 14:13 -0700
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-16 13:23 -0700
                Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-03-15 14:16 -0700
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-15 14:26 -0700
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-15 14:30 -0700
                Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-03-15 15:48 -0700
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-17 13:41 -0700
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-17 21:49 -0700
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-16 01:16 +0000
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-16 19:08 +0200
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-16 17:22 +0000
                Re: Radians Or Degrees? scott@slp53.sl.home (Scott Lurndal) - 2024-03-16 18:32 +0000
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-16 20:49 +0200
                Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-03-16 16:19 -0700
                Re: Radians Or Degrees? bart <bc@freeuk.com> - 2024-03-17 00:00 +0000
                Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-03-16 18:38 -0700
                Re: Radians Or Degrees? bart <bc@freeuk.com> - 2024-03-17 01:57 +0000
                Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-03-16 19:57 -0700
                Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-03-17 13:10 +0100
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-17 11:06 +0200
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-17 11:34 +0200
                Re: Radians Or Degrees? bart <bc@freeuk.com> - 2024-03-17 10:59 +0000
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-17 14:15 +0200
                Re: Radians Or Degrees? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-15 15:13 -0700
                Re: Radians Or Degrees? Stefan Monnier <monnier@iro.umontreal.ca> - 2024-03-18 15:18 -0400
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-18 22:19 +0000
                Re: Radians Or Degrees? Stefan Monnier <monnier@iro.umontreal.ca> - 2024-03-20 09:54 -0400
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-20 18:21 +0200
                Re: Radians Or Degrees? Stefan Monnier <monnier@iro.umontreal.ca> - 2024-03-20 12:59 -0400
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-20 20:40 +0000
                Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-03-21 08:52 +0100
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-21 14:51 +0200
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-21 16:37 +0000
                Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-03-23 09:11 +0100
                Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-03-20 17:02 +0000
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-20 20:47 +0000
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-20 20:33 +0000
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-03-21 00:03 +0200
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-20 20:26 +0000
                Re: Radians Or Degrees? Stefan Monnier <monnier@iro.umontreal.ca> - 2024-03-20 16:34 -0400
                Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-03-21 08:38 +0100
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-02-23 14:32 +0200
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-02-23 20:02 +0000
                Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-23 20:38 +0000
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-02-23 22:29 +0000
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-23 22:39 +0000
                Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-24 04:03 +0000
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-24 04:47 +0000
                Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-24 05:27 +0000
                Re: Radians Or Degrees? Kaz Kylheku <433-929-6894@kylheku.com> - 2024-02-24 05:48 +0000
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-24 05:38 +0000
                Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-24 06:13 +0000
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-03-14 17:15 +0000
                Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-23 23:20 +0000
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-23 22:39 +0000
                Re: Radians Or Degrees? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-02-23 23:16 +0000
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-23 23:44 +0000
                Re: Radians Or Degrees? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-02-24 01:15 +0000
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-24 01:19 +0000
                Re: Radians Or Degrees? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-02-24 01:27 +0000
                Re: Radians Or Degrees? Kaz Kylheku <433-929-6894@kylheku.com> - 2024-02-24 01:42 +0000
                Re: Radians Or Degrees? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-02-25 00:18 +0000
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-02-25 12:57 +0200
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-24 02:21 +0000
                Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-24 02:49 +0000
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-24 03:07 +0000
                Re: Radians Or Degrees? Kaz Kylheku <433-929-6894@kylheku.com> - 2024-02-24 03:12 +0000
                Re: Radians Or Degrees? Tim Rentsch <tr.17687@z991.linuxsc.com> - 2024-02-23 18:49 -0800
                Re: Radians Or Degrees? Kaz Kylheku <433-929-6894@kylheku.com> - 2024-02-23 23:30 +0000
                Re: Radians Or Degrees? James Kuyper <jameskuyper@alumni.caltech.edu> - 2024-02-24 02:25 -0500
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-24 21:21 +0000
                Re: Radians Or Degrees? James Kuyper <jameskuyper@alumni.caltech.edu> - 2024-02-24 17:32 -0500
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-24 22:50 +0000
                Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-02-25 16:19 +0100
                Re: Radians Or Degrees? mitchalsup@aol.com (MitchAlsup1) - 2024-02-25 18:11 +0000
                Re: Radians Or Degrees? Terje Mathisen <terje.mathisen@tmsw.no> - 2024-02-23 11:01 +0100
                Re: Radians Or Degrees? "Steven G. Kargl" <sgk@REMOVEtroutmask.apl.washington.edu> - 2024-02-22 22:09 +0000
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 22:30 +0000
                Re: Radians Or Degrees? Michael S <already5chosen@yahoo.com> - 2024-02-23 00:56 +0200
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 23:03 +0000
  Re: Radians Or Degrees? fir <fir@grunge.pl> - 2024-02-22 00:15 +0100
    Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 01:55 +0000
      Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-22 09:32 +0100
        Re: Radians Or Degrees? Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2024-02-22 09:38 +0000
          Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-22 11:04 +0100
      Re: Radians Or Degrees? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-02-22 14:28 +0000
        Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-22 16:26 +0100
          Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 19:45 +0000
          Re: Radians Or Degrees? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-02-22 21:30 +0000
            Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-23 09:11 +0100
        GGs [was Radians Or Degrees?] Richard Harnden <richard.nospam@gmail.invalid> - 2024-02-23 13:57 +0000
          Re: GGs [was Radians Or Degrees?] "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-23 11:15 -0800
            Re: GGs [was Radians Or Degrees?] Richard Harnden <richard.nospam@gmail.invalid> - 2024-02-23 19:26 +0000
  Re: Radians Or Degrees? Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2024-02-22 07:17 +0000
    Re: Radians Or Degrees? Kaz Kylheku <433-929-6894@kylheku.com> - 2024-02-22 16:49 +0000
  Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-22 09:06 +0100
  Re: Radians Or Degrees? Blue-Maned_Hawk <bluemanedhawk@invalid.invalid> - 2024-02-22 08:27 +0000
    Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-22 11:09 +0100
      Re: Radians Or Degrees? Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2024-02-22 13:48 +0000
      Re: Radians Or Degrees? Blue-Maned_Hawk <bluemanedhawk@invalid.invalid> - 2024-02-22 15:29 +0000
        Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-22 20:02 +0100
          Re: Radians Or Degrees? Blue-Maned_Hawk <bluemanedhawk@invalid.invalid> - 2024-02-23 02:15 +0000
          Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-23 02:24 +0000
            Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-23 09:16 +0100
      Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 19:39 +0000
        Re: Radians Or Degrees? Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2024-02-22 21:25 +0100
          Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 20:58 +0000
            Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-23 09:33 +0100
              Re: Radians Or Degrees? Janis Papanagnou <janis_papanagnou+ng@hotmail.com> - 2024-02-23 12:53 +0100
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-23 20:23 +0000
        Re: Radians Or Degrees? Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2024-02-25 11:19 +0000
          Re: Radians Or Degrees? Richard Harnden <richard.nospam@gmail.invalid> - 2024-02-25 13:08 +0000
            Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-25 22:21 +0000
              Re: Radians Or Degrees? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2024-02-25 22:29 +0000
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-26 21:29 +0000
                Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-02-26 13:44 -0800
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-26 23:15 +0000
                Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-02-26 16:02 -0800
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-27 00:55 +0000
                Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-27 09:53 +0100
              Re: Radians Or Degrees? Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2024-02-25 14:43 -0800
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-26 21:32 +0000
              Re: Radians Or Degrees? bart <bc@freeuk.com> - 2024-02-25 23:09 +0000
                Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-26 21:32 +0000
                Re: Radians Or Degrees? bart <bc@freeuk.com> - 2024-02-26 23:01 +0000
                Re: Radians Or Degrees? David Brown <david.brown@hesbynett.no> - 2024-02-27 09:59 +0100
      Re: Radians Or Degrees? Lawrence D'Oliveiro <ldo@nz.invalid> - 2024-02-22 19:44 +0000

csiph-web