1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
|
% proflycee-tools-trigo.tex
% Copyright 2023-2024 Cédric Pierquet
% Released under the LaTeX Project Public License v1.3c or later, see http://www.latex-project.org/lppl.txt
%%------CercleTrigo
\defKV[cercletrigo]{%
Rayon=\def\PLcerclerayon{#1},%
Epaisseur=\def\PLcerclethick{#1},%
EpaisseurSol=\def\PLcerclesolthick{#1},%
Marge=\def\PLcerclemarge{#1},%
TailleValeurs=\def\PLcerclevaleurs{#1},%
TailleAngles=\def\PLcercleangles{#1},%
CouleurFond=\def\PLcerclefond{#1},%
Decal=\def\PLcercledecal{#1},%
cos=\def\PLcerclevalcos{#1},%
sin=\def\PLcerclevalsin{#1},%
CouleurSol=\def\PLcerclecoleq{#1}
}
\setKVdefault[cercletrigo]{
Rayon=3,%
Marge=0.25,%
Decal=10pt,%
Epaisseur=thick,%
EpaisseurSol=very thick,%
AffAngles=true,%
AffTraits=true,%
AffTraitsEq=true,%
AffValeurs=true,%
MoinsPi=true,%
TailleValeurs=\scriptsize,%
TailleAngles=\footnotesize,%
CouleurFond=white,%
Equationcos=false,%
Equationsin=false,%
cos=45,%
sin=30,%
CouleurSol=blue
}
\newcommand\CercleTrigo[1][]{%
\useKVdefault[cercletrigo]
\setKV[cercletrigo]{#1}
\tikzset{PLval/.style={inner sep=1pt,font=\PLcerclevaleurs,fill=\PLcerclefond}}
\tikzset{PLagl/.style={inner sep=1pt,font=\PLcercleangles,fill=\PLcerclefond}}
%valeurs remarquables
\ifboolKV[cercletrigo]{AffAngles}
{%valeursdudessus
\draw ({\PLcerclerayon},0) node[above right=2pt,font=\PLcercleangles] {0} ;
\draw ($(30:{\PLcerclerayon})+(30:\PLcercledecal)$) node[PLagl] {$\tfrac{\pi}{6}$} ;
\draw ($(45:{\PLcerclerayon})+(45:\PLcercledecal)$) node[PLagl] {$\tfrac{\pi}{4}$} ;
\draw ($(60:{\PLcerclerayon})+(60:\PLcercledecal)$) node[PLagl] {$\tfrac{\pi}{3}$} ;
\draw (0,{\PLcerclerayon}) node[above right=2pt,PLagl] {$\tfrac{\pi}{2}$} ;
\draw ({-\PLcerclerayon},0) node[above left=2pt,PLagl] {$\pi$} ;
\draw ($(150:{\PLcerclerayon})+(150:\PLcercledecal)$) node[PLagl] {$\tfrac{5\pi}{6}$} ;
\draw ($(135:{\PLcerclerayon})+(135:\PLcercledecal)$) node[PLagl] {$\tfrac{3\pi}{4}$} ;
\draw ($(120:{\PLcerclerayon})+(120:\PLcercledecal)$) node[PLagl] {$\tfrac{2\pi}{3}$} ;
\draw ($(30:{\PLcerclerayon})+(30:\PLcercledecal)$) node[PLagl] {$\tfrac{\pi}{6}$} ;
%valeursdudessous
\draw ($(-30:{\PLcerclerayon})+(-30:\PLcercledecal)$) node[PLagl] {$\tfrac{\ifboolKV[cercletrigo]{MoinsPi}{-}{11}\pi}{6}$} ;
\draw ($(-45:{\PLcerclerayon})+(-45:\PLcercledecal)$) node[PLagl] {$\tfrac{\ifboolKV[cercletrigo]{MoinsPi}{-}{7}\pi}{4}$} ;
\draw ($(-60:{\PLcerclerayon})+(-60:\PLcercledecal)$) node[PLagl] {$\tfrac{\ifboolKV[cercletrigo]{MoinsPi}{-}{5}\pi}{3}$} ;
\draw (0,{-\PLcerclerayon}) node[below right=2pt,PLagl] {$\tfrac{\ifboolKV[cercletrigo]{MoinsPi}{-}{3}\pi}{2}$} ;
\draw ($(-120:{\PLcerclerayon})+(-120:\PLcercledecal)$) node[PLagl] {$\tfrac{\ifboolKV[cercletrigo]{MoinsPi}{-2}{4}\pi}{3}$} ;
\draw ($(-135:{\PLcerclerayon})+(-135:\PLcercledecal)$) node[PLagl] {$\tfrac{\ifboolKV[cercletrigo]{MoinsPi}{-3}{5}\pi}{4}$} ;
\draw ($(-150:{\PLcerclerayon})+(-150:\PLcercledecal)$) node[PLagl] {$\tfrac{\ifboolKV[cercletrigo]{MoinsPi}{-5}{7}\pi}{6}$} ;
\ifboolKV[cercletrigo]{MoinsPi}
{\draw ({-\PLcerclerayon},0) node[below left=2pt,PLagl] {$-\pi$} ;}
{\draw ({\PLcerclerayon},0) node[below right=2pt,PLagl] {$2\pi$} ;}
}%
{}
%tracés
\draw[\PLcerclethick,->,>=latex] ({-\PLcerclerayon-\PLcerclemarge},0)--({\PLcerclerayon+\PLcerclemarge},0) ;
\draw[\PLcerclethick,->,>=latex] (0,{-\PLcerclerayon-\PLcerclemarge})--(0,{\PLcerclerayon+\PLcerclemarge}) ;
\draw[\PLcerclethick] (0,0) circle[radius=\PLcerclerayon] ;
\draw (0,0) node[below left=2pt,PLval] {0} ;
%equations
\ifboolKV[cercletrigo]{Equationcos}
{%traitsdeconstructioncos
\ifboolKV[cercletrigo]{AffTraitsEq}
{%
\draw[\PLcerclethick,dotted,gray] (-45:\PLcerclerayon) -- (135:\PLcerclerayon)
(-135:\PLcerclerayon) -- (45:\PLcerclerayon)
(30:\PLcerclerayon) -- (150:\PLcerclerayon)
(-30:\PLcerclerayon) -- (-150:\PLcerclerayon)
(-60:\PLcerclerayon)--(60:\PLcerclerayon)
(-120:\PLcerclerayon)--(120:\PLcerclerayon) ;
}{}%
\draw[\PLcerclesolthick,\PLcerclecoleq] ({\PLcerclevalcos}:\PLcerclerayon)--({-\PLcerclevalcos}:\PLcerclerayon) ;
\filldraw[\PLcerclecoleq] ({\PLcerclevalcos}:\PLcerclerayon) circle[radius=2pt] ({-\PLcerclevalcos}:\PLcerclerayon) circle[radius=2pt] ;%
}
{}
\ifboolKV[cercletrigo]{Equationsin}
{%traitsdeconstructioncos
\ifboolKV[cercletrigo]{AffTraitsEq}
{%
\draw[\PLcerclethick,dotted,gray] (-45:\PLcerclerayon) -- (135:\PLcerclerayon)
(-135:\PLcerclerayon) -- (45:\PLcerclerayon)
(30:\PLcerclerayon) -- (150:\PLcerclerayon)
(-30:\PLcerclerayon) -- (-150:\PLcerclerayon)
(-60:\PLcerclerayon)--(60:\PLcerclerayon)
(-120:\PLcerclerayon)--(120:\PLcerclerayon) ;
}{}%
\draw[\PLcerclesolthick,\PLcerclecoleq] ({\PLcerclevalsin}:\PLcerclerayon)--({180-\PLcerclevalsin}:\PLcerclerayon) ;
\filldraw[\PLcerclecoleq] ({\PLcerclevalsin}:\PLcerclerayon) circle[radius=2pt] ({180-\PLcerclevalsin}:\PLcerclerayon) circle[radius=2pt] ;%
}
{}
%valeurs
\ifboolKV[cercletrigo]{AffValeurs}
{%
\draw ({0.5*\PLcerclerayon},0) node[below=2pt,PLval] {$\tfrac{1}{2}$} ;
\draw ({-0.5*\PLcerclerayon},0) node[below=2pt,PLval] {$-\tfrac{1}{2}$} ;
\draw (0,{0.5*\PLcerclerayon}) node[left=2pt,PLval] {$\tfrac{1}{2}$} ;
\draw (0,{-0.5*\PLcerclerayon}) node[left=2pt,PLval] {$-\tfrac{1}{2}$} ;
\draw ({0.866*\PLcerclerayon},0) node[below=2pt,PLval] {$\tfrac{\sqrt{3}}{2}$} ;
\draw ({-0.866*\PLcerclerayon},0) node[below=2pt,PLval] {$-\tfrac{\sqrt{3}}{2}$} ;
\draw (0,{0.866*\PLcerclerayon}) node[left=2pt,PLval] {$\tfrac{\sqrt{3}}{2}$} ;
\draw (0,{-0.866*\PLcerclerayon}) node[left=2pt,PLval] {$-\tfrac{\sqrt{3}}{2}$} ;
\draw ({0.707*\PLcerclerayon},0) node[above=2pt,PLval] {$\tfrac{\sqrt{2}}{2}$} ;
\draw ({-0.707*\PLcerclerayon},0) node[above=2pt,PLval] {$-\tfrac{\sqrt{2}}{2}$} ;
\draw (0,{0.707*\PLcerclerayon}) node[right=2pt,PLval] {$\tfrac{\sqrt{2}}{2}$} ;
\draw (0,{-0.707*\PLcerclerayon}) node[right=2pt,PLval] {$-\tfrac{\sqrt{2}}{2}$} ;
%\draw[\PLcerclethick] (0,0) circle[radius=\PLcerclerayon] ; %on retrace par dessus ?
}%
{}
%valeurs remarquables en dernier
\ifboolKV[cercletrigo]{AffTraits}
{%
\draw[\PLcerclethick,dotted,gray] (-120:\PLcerclerayon) rectangle (60:\PLcerclerayon) ;
\draw[\PLcerclethick,dotted,gray] (-150:\PLcerclerayon) rectangle (30:\PLcerclerayon) ;
\draw[\PLcerclethick,dotted,gray] (-135:\PLcerclerayon) rectangle (45:\PLcerclerayon) ;
\draw[\PLcerclethick,dotted,gray] (-120:\PLcerclerayon)--(60:\PLcerclerayon) ;
\draw[\PLcerclethick,dotted,gray] (-150:\PLcerclerayon)--(30:\PLcerclerayon) ;
\draw[\PLcerclethick,dotted,gray] (-135:\PLcerclerayon)--(45:\PLcerclerayon) ;
\draw[\PLcerclethick,dotted,gray] (120:\PLcerclerayon)--(-60:\PLcerclerayon) ;
\draw[\PLcerclethick,dotted,gray] (150:\PLcerclerayon)--(-30:\PLcerclerayon) ;
\draw[\PLcerclethick,dotted,gray] (135:\PLcerclerayon)--(-45:\PLcerclerayon) ;
}%
{}
}
%%------MESUREPPALE
\setKVdefault[MesurePpale]{%
Crochets=false,%
d=false,%
Brut=false
}
\newcommand{\MesurePrincipale}[2][]{%fraction sous la forme a*pi/b ou entier :-)
\useKVdefault[MesurePpale]%
\setKV[MesurePpale]{#1}%
\StrDel{#2}{pi}[\MPargument]%
\IfBeginWith{#2}{pi}%
{\StrSubstitute{#2}{pi}{1}[\MPargument]}%
{}%
\IfBeginWith{#2}{-pi}%
{\StrSubstitute{#2}{pi}{1}[\MPargument]}%
{}%
%on conserve les données initiales
\IfSubStr{\MPargument}{/}%on coupe numérateur/dénominateur
{ \StrCut{\MPargument}{/}\MPnumerateurinit\MPdenominateurinit }%
{ \xdef\MPnumerateurinit{\MPargument}\xdef\MPdenominateurinit{1} }%
%on affiche le début, avant simplification
\ifboolKV[MesurePpale]{d}%
{\displaystyle}%
{}%
\xintifboolexpr{\MPdenominateurinit == 1}%
{\ifboolKV[MesurePpale]{Brut}{}{\num{\MPnumerateurinit}\pi=}}%
{\ifboolKV[MesurePpale]{Brut}{}{\frac{\num{\MPnumerateurinit}\pi}{\num{\MPdenominateurinit}}=}}%
%on simplifie puis on réduit
\xdef\MPsimpl{\xintPRaw{\xintIrr{\MPargument}}}%
%test si l'argument est une fraction ou un entier
\IfSubStr{\MPsimpl}{/}%
{\StrCut{\MPsimpl}{/}\MPnumerateur\MPdenominateur}%
{\xdef\MPnumerateur{\MPsimpl}\xdef\MPdenominateur{1}}%
%calculs
\xdef\MPtour{\inteval{2*\MPdenominateur}}%
\xdef\MPreste{\xintiiRem{\MPnumerateur}{\MPtour}}%reste
\xintifboolexpr{\MPreste>\MPdenominateur}%
{\xdef\MPreste{\inteval{\MPreste-\MPtour}}}{}%
\xintifboolexpr{\MPreste<-\MPdenominateur}%
{\xdef\MPreste{\inteval{\MPreste+\MPtour}}}{}%
%sortie suivant fraction ou non...
\xintifboolexpr{\MPdenominateur == 1}%
{%entier
\xintifboolexpr{\MPreste == 1}{\pi \ifboolKV[MesurePpale]{Brut}{}{\: \ifboolKV[MesurePpale]{Crochets}{[2\pi]}{(2\pi)}} }{}%
\xintifboolexpr{\MPreste == 0}{0 \ifboolKV[MesurePpale]{Brut}{}{\: \ifboolKV[MesurePpale]{Crochets}{[2\pi]}{(2\pi)}} }{}%
\xintifboolexpr{\MPreste != 0 && \MPreste != 1}{\MPreste\pi \ifboolKV[MesurePpale]{Brut}{}{\: \ifboolKV[MesurePpale]{Crochets}{[2\pi]}{(2\pi)}} }{}%
}%
{%fraction
\frac{%
\xintifboolexpr{\xinteval{\MPreste == 1}}{}{}%
\xintifboolexpr{\xinteval{\MPreste == -1}}{-}{}%
\xintifboolexpr{\xinteval{abs(\MPreste) != 1}}{\num{\MPreste}}{}%
\pi}{\num{\MPdenominateur}} \ifboolKV[MesurePpale]{Brut}{}{\: \ifboolKV[MesurePpale]{Crochets}{[2\pi]}{(2\pi)}}%
}%
}
%%------LIGNES TRIGOS
\setKVdefault[Lgntrig]{%
d=false,%
Etapes=false
}
\newcommand\AffAngle[2][]{%semble OK
%1 = options
%2 = angle sous la forme a*pi/b
\useKVdefault[Lgntrig]%
\setKV[Lgntrig]{#1}%
\StrDel{#2}{pi}[\MPargument]%
\IfBeginWith{#2}{pi}%
{\StrSubstitute{#2}{pi}{1}[\MPargument]}%
{}%
\IfBeginWith{#2}{-pi}%
{\StrSubstitute{#2}{pi}{1}[\MPargument]}%
{}%
%on conserve les données initiales
\IfSubStr{\MPargument}{/}%on coupe numérateur/dénominateur
{\StrCut{\MPargument}{/}\MPnumerateurinit\MPdenominateurinit}%
{\xdef\MPnumerateurinit{\MPargument}\xdef\MPdenominateurinit{1}}%
%on affiche le début, avant simplification
\ifboolKV[Lgntrig]{d}{\displaystyle}{}%
\xintifboolexpr{\MPdenominateurinit == 1}%
{%
\xintifboolexpr{\MPnumerateurinit == 1}{\pi}{}%
\xintifboolexpr{\MPnumerateurinit == -1}{-\pi}{}%
\xintifboolexpr{\xinteval{abs(\MPnumerateurinit) != 1}}{\num{\MPnumerateurinit}\pi}{}%
}%
{%
\frac{%
\xintifboolexpr{\MPnumerateurinit == 1}{\pi}{}%
\xintifboolexpr{\MPnumerateurinit == -1}{-\pi}{}
\xintifboolexpr{\xinteval{abs(\MPnumerateurinit) != 1}}{\num{\MPnumerateurinit}\pi}{}%
}%
{%
\num{\MPdenominateurinit}%
}%
}%
}
\newcommand\IntSimplifMesPpale[1]{%commande interne
\IfSubStr{#1}{pi}%
{%
\StrDel{#1}{pi}[\tmpargument]
\IfBeginWith{#1}{pi}%
{\StrSubstitute{#1}{pi}{1}[\tmpargument]}%
{}%
\IfBeginWith{#1}{-pi}%
{\StrSubstitute{#1}{pi}{1}[\tmpargument]}%
{}%
}%
{\def\tmpargument{#1}}%
\IfSubStr{\tmpargument}{/}%on coupe numérateur/dénominateur
{\StrCut{\tmpargument}{/}\MPnumerateurinit\MPdenominateurinit}%
{\xdef\MPnumerateurinit{\tmpargument}\xdef\MPdenominateurinit{1}}%
\xdef\MPsimpl{\xintPRaw{\xintIrr{\tmpargument}}}%
\IfSubStr{\MPsimpl}{/}%
{\StrCut{\MPsimpl}{/}\MPnumerateur\MPdenominateur}%
{\xdef\MPnumerateur{\MPsimpl}\xdef\MPdenominateur{1}}%
%calculs
\xdef\MPtour{\inteval{2*\MPdenominateur}}%
\xdef\MPreste{\xintiiRem{\MPnumerateur}{\MPtour}}%reste
\xintifboolexpr{\MPreste>\MPdenominateur}%
{\xdef\MPreste{\inteval{\MPreste-\MPtour}}}{}%
\xintifboolexpr{\MPreste<-\MPdenominateur}%
{\xdef\MPreste{\inteval{\MPreste+\MPtour}}}{}%
\xdef\MPfrac{\MPreste/\MPdenominateur}%
}
\NewDocumentCommand\LigneTrigo{ s O{} m d() }{%
%* = sans l'énoncé
%2 = options
%3 = ligne
%4 = angle
\useKVdefault[Lgntrig]%
\setKV[Lgntrig]{#2}
\ifboolKV[Lgntrig]{d}{\displaystyle}{}%
\IntSimplifMesPpale{#4} %simplification du quotient et stockage dans \MPfrac
%les cas de figure [0;pi]
\xintifboolexpr{\MPfrac == 0}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 1 }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 0 }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 0 }{}%
}%
{}%
\xintifboolexpr{\MPfrac == 1/12}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{6}+\sqrt{2}}{4} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left(\MesurePrincipale[Brut]{#4}\right)}=}{} \frac{\sqrt{6}-\sqrt{2}}{4} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 2-\sqrt{3} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == 1/6}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{3}}{2} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{1}{2} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{3}}{3} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == 1/4}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{2}}{2} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{2}}{2} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 1 }{}%
}%
{}%
\xintifboolexpr{\MPfrac == 1/3}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{1}{2} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{3}}{2} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \sqrt{3} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == 5/12}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{6}-\sqrt{2}}{4} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{6}+\sqrt{2}}{4} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 2+\sqrt{3} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == 1/2}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 0 }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 1 }{}%
}%
{}%
\xintifboolexpr{\MPfrac == 7/12}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-\sqrt{6}+\sqrt{2}}{4} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{6}+\sqrt{2}}{4} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -2-\sqrt{3} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == 2/3}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{1}{2} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{3}}{2} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\sqrt{3} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == 3/4}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{2}}{2} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{2}}{2} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -1 }{}%
}%
{}%
\xintifboolexpr{\MPfrac == 5/6}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{3}}{2} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{1}{2} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{3}}{3} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == 11/12}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-\sqrt{6}-\sqrt{2}}{4} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{6}-\sqrt{2}}{4} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -2+\sqrt{3} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == 1}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -1 }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 0 }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 0 }{}%
}%
{}%
\xintifboolexpr{\MPfrac == 1/8}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{2+\sqrt{2}}}{2} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{2-\sqrt{2}}}{2} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -1+\sqrt{2} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == 3/8}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{2-\sqrt{2}}}{2} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{2+\sqrt{2}}}{2} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 1+\sqrt{2} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == 5/8}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{2-\sqrt{2}}}{2} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{2+\sqrt{2}}}{2} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -1-\sqrt{2} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == 7/8}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{2+\sqrt{2}}}{2} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{2-\sqrt{2}}}{2} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 1-\sqrt{2} }{}%
}%
{}%
%cas ]-pi,0[
\xintifboolexpr{\MPfrac == -1/12}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{6}+\sqrt{2}}{4} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-\sqrt{6}+\sqrt{2}}{4} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -2+\sqrt{3} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == -1/6}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{3}}{2} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{1}{2} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{3}}{3} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == -1/4}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{2}}{2} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{2}}{2} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -1 }{}%
}%
{}%
\xintifboolexpr{\MPfrac == -1/3}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{1}{2} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{3}}{2} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\sqrt{3} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == -5/12}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{6}-\sqrt{2}}{4} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-\sqrt{6}-\sqrt{2}}{4} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -2-\sqrt{3} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == -1/2}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 0 }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -1 }{}%
}%
{}%
\xintifboolexpr{\MPfrac == -7/12}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-\sqrt{6}+\sqrt{2}}{4} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-\sqrt{6}-\sqrt{2}}{4} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 2+\sqrt{3} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == -2/3}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{1}{2} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{3}}{2} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \sqrt{3} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == -3/4}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{2}}{2} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{2}}{2} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 1 }{}%
}%
{}%
\xintifboolexpr{\MPfrac == -5/6}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{3}}{2} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{1}{2} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{3}}{3} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == -11/12}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-\sqrt{6}-\sqrt{2}}{4} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-\sqrt{6}+\sqrt{2}}{4} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 2-\sqrt{3} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == -1/8}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{2+\sqrt{2}}}{2} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{2-\sqrt{2}}}{2} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 1-\sqrt{2} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == -3/8}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{2-\sqrt{2}}}{2} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{2+\sqrt{2}}}{2} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -1-\sqrt{2} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == -5/8}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{2-\sqrt{2}}}{2} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{2+\sqrt{2}}}{2} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} 1+\sqrt{2} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == -7/8}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{2+\sqrt{2}}}{2} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{2-\sqrt{2}}}{2} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -1+\sqrt{2} }{}%
}%
{}%
%les pi/5
\xintifboolexpr{\MPfrac == 1/5}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{1+\sqrt{5}}{4} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{10-2\sqrt{5}}}{4} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \sqrt{5-2\sqrt{5}} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == 2/5}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-1+\sqrt{5}}{4} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{10+2\sqrt{5}}}{4} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \sqrt{5+2\sqrt{5}} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == 3/5}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{1-\sqrt{5}}{4} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{10+2\sqrt{5}}}{4} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\sqrt{5+2\sqrt{5}} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == 4/5}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-1-\sqrt{5}}{4} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{10-2\sqrt{5}}}{4} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\sqrt{5-2\sqrt{5}} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == -4/5}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-1-\sqrt{5}}{4} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{10-2\sqrt{5}}}{4} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \sqrt{5-2\sqrt{5}} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == -3/5}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{1-\sqrt{5}}{4} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{10+2\sqrt{5}}}{4} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \sqrt{5+2\sqrt{5}} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == -2/5}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-1+\sqrt{5}}{4} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{10+2\sqrt{5}}}{4} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\sqrt{5+2\sqrt{5}} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == -1/5}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{1+\sqrt{5}}{4} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{10-2\sqrt{5}}}{4} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\sqrt{5-2\sqrt{5}} }{}%
}%
{}%
%les pi/10
\xintifboolexpr{\MPfrac == 1/10}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{10+2\sqrt{5}}}{4} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-1+\sqrt{5}}{4} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{25-10\sqrt{5}}}{5} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == 3/10}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{10-2\sqrt{5}}}{4} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{1+\sqrt{5}}{4} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{25+10\sqrt{5}}}{5} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == 7/10}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{10-2\sqrt{5}}}{4} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{1+\sqrt{5}}{4} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{25+10\sqrt{5}}}{5} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == 9/10}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{10+2\sqrt{5}}}{4} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{-1+\sqrt{5}}{4} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{25-10\sqrt{5}}}{5} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == -1/10}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{10+2\sqrt{5}}}{4} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{1-\sqrt{5}}{4} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{25-10\sqrt{5}}}{5} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == -3/10}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{10-2\sqrt{5}}}{4} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{1+\sqrt{5}}{4} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{25+10\sqrt{5}}}{5} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == -7/10}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{10-2\sqrt{5}}}{4} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{1+\sqrt{5}}{4} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{25+10\sqrt{5}}}{5} }{}%
}%
{}%
\xintifboolexpr{\MPfrac == -9/10}
{%
\ifstrequal{#3}{cos}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\cos}{\left({\AffAngle[#2]{#4}}\right)}=}{\cos}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} -\frac{\sqrt{10+2\sqrt{5}}}{4} }{}%
\ifstrequal{#3}{sin}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\sin}{\left({\AffAngle[#2]{#4}}\right)}=}{\sin}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{1-\sqrt{5}}{4} }{}%
\ifstrequal{#3}{tan}%
{\ifboolKV[Lgntrig]{Etapes}{\IfBooleanTF{#1}{}{{\tan}{\left({\AffAngle[#2]{#4}}\right)}=}{\tan}{\left({\MesurePrincipale[Brut]{#4}}\right)}=}{} \frac{\sqrt{25-10\sqrt{5}}}{5} }{}%
}%
{}%
}
\endinput
|