symbolic math - Maxima: trigonometric numbers in radical form -


beginner's question maxima: how can obtain trigonometric numbers in radical form?

for example, expression evaluates nicely:

(%i) cos( 3 * %pi / 4);                                        1 (%o)                              - -------                                     sqrt(2)

but 1 not:

(%i) cos(3 * %pi / 5);                                      3 %pi (%o)                             cos(-----)                                        5

i expect show this:

(%i) cos( 3 * %pi / 5);                                   1 - sqrt(5) (%o)                              -----------                                        4

see, example, output wolfram alpha:

http://www.wolframalpha.com/input/?i=cos%283+pi+%2f+5%29

from maxima documentation piargs, true default:

when %piargs true, trigonometric functions simplified algebraic constants when argument integer multiple of %pi, %pi/2, %pi/3, %pi/4, or %pi/6.

from maxima documentation ntrig:

the ntrig package contains set of simplification rules used simplify trigonometric function arguments of form f(n%pi/10) f of functions sin, cos, tan, csc, sec , cot.

this work 3π/5, not more complex values π/96:

(%i) load(ntrig); (%o)        /usr/share/maxima/5.34.1/share/trigonometry/ntrig.mac (%i) cos(3*%pi/5);                                  1 - sqrt(5) (%o)                             -----------                                       4 (%i) sin(4*%pi/10);                              sqrt(sqrt(5) + 5) (%o)                         -----------------                                     3/2                                    2 (%i) sin(%pi/96);                                       %pi (%o)                              sin(---)                                       96

to evaluate more complex results, trigeval function trigtools package work:

(%i) load(trigtools); (%o)   /usr/share/maxima/5.34.1/share/contrib/trigtools/trigtools.mac (%i) trigeval(sin(4*%pi/10));                               sqrt(sqrt(5) + 5) (%o)                          -----------------                                      3/2                                     2 (%i) trigeval(sin(%pi/96));                    9/8                        3/2         5/4              sqrt(2    - sqrt(sqrt(sqrt(3) + 2    + 1) + 2   )) (%o)         --------------------------------------------------                                     17/16                                    2

there documentation trigtools, because part of 3rd-party contrib packages, not maintained. source code trigtools hasn't been updated since 2013.

also, trigeval seems work angles corresponding regular polygons, , not trigonometric numbers in general. example, cos (π / 23) = -(1/2)(-1)22/23(1+(-1)2/23), trigeval unhelpful in case:

(%i) trigeval(cos(%pi/23));                                       %pi (%o)                              cos(---)                                       23

credit goes serge de marre , raymond toy on maxima-discuss mailing list, david billinghurst on maxima area 51 stackexchange.

relevant links other mailing lists:


-

Comments

Post a Comment

Popular posts from this blog

javascript - Thinglink image not visible until browser resize -

Image
i trying repurpose pre-existing theme, includes drop down menu displays image. trying embed thinglink drop down menu's content section, not visible until resize browser window. here menu looks like: then when clicked, can see empty space image should show: then when browser resized, image appears: this code content of menu: <div class="ajax_accordion_content" style="display: none;"> <div class="report-detail"> <table border="0" cellpadding="0" cellspacing="0" width="100%" class="table_basic"> <tbody> <!-- thinglink image embedded --> <img style="max-width: 100%;" src="http://cdn.thinglink.me/api/image/832705713204625409/1024/10/scaletowidth#tl-832705713204625409;1043138249'" class="alwaysthinglink"/> <script async charset="utf-8" src="http://cdn.thinglink.me/jse/embed.j...
Read more

firebird - Error "invalid transaction handle (expecting explicit transaction start)" executing script from Delphi -

i'm developing update app delphi 10. i'm running windows 7 64x, firebird 2.5.1.26351 32x. execution order: checks current version(select statement firebird database) downloads update(via ftp) apply it(.exe files, , execute .sql) error code -901 pops out when try execute .sql files. know there incompatibility issue w7 64x , fdb 32x, but, can everything: backup , restore(gbak), db commands(all). tried fdb 64x instead, , not working. code: //components fdwaitcursor: tfdguixwaitcursor; fddriverlink: tfdphysfbdriverlink; fdconnection:tfdconnection; fdscript: tfdscript; function tthr_script.createcomponents:boolean; begin try fddriverlink := tfdphysfbdriverlink.create(fddriverlink); fdwaitcursor := tfdguixwaitcursor.create(fdwaitcursor); fdconnection := tfdconnection.create(fdconnection); fdconnection begin drivername := 'fb'; params.username := thrbanco.bduser; params.password := thrbanco.bdpass; params.database := ...
Read more

Sound is not coming out while implementing Text-to-speech in Android activity -

i using texttospeak in 1 of app. while adding speech string texttospeech object instance, doesn't produce sound. though not getting error in log still sound not coming out. want device speak value of textview gets set resultmsg.settext() method. public class resultactivity extends activity { @override protected void oncreate(bundle savedinstancestate){ ............ resultmsg.settext(resultmsg_str); texttospeech = new texttospeech(getapplicationcontext(),newtexttospeech.oninitlistener(){ @override public void oninit(int status) { system.out.println("txt speech status = "+status); system.out.println("txt speech error status = "+texttospeech.error); system.out.println("txt speech success status = "+texttospeech.success); if(status == texttospeech.success){ texttospeech.setlanguage(locale.english); ...
Read more