WEBVTT

00:00:00.340 --> 00:00:03.360
Ja es tev pieietu uz ielas un pajautātu –

00:00:03.360 --> 00:00:07.450
tik treknā šriftā negribēju rakstīt –

00:00:07.450 --> 00:00:11.710
saki, lūdzu, cik ir sīnuss
no pī dalīts ar 4, –

00:00:11.710 --> 00:00:14.950
un mēs, protams, runājam par vērtību radiānos –

00:00:14.950 --> 00:00:17.510
tu to būsi vai nu iemācījies no galvas,

00:00:17.510 --> 00:00:19.920
vai uzzīmēsi vienības riņķi,
lai atrastu atbildi.

00:00:19.920 --> 00:00:21.360
Nav pats skaistākais vienības riņķis,
bet priekšstatam derēs.

00:00:21.360 --> 00:00:23.080


00:00:23.080 --> 00:00:26.960
Tu atliktu leņķi ar platumu
pī dalīts ar 4 radiāni,

00:00:26.960 --> 00:00:29.760
kas ir tas pats, kas 45 grādu leņķis.

00:00:29.760 --> 00:00:31.840
Atbilstošajā riņķa vietā
tu novilktu rādiusu.

00:00:31.840 --> 00:00:35.130
Un sinuss ir šī punkta y koordināta
vienības riņķī.

00:00:35.130 --> 00:00:36.250


00:00:36.250 --> 00:00:38.910
Tātad mēs gribam noskaidrot šo te vērtību.

00:00:38.910 --> 00:00:40.210
Mums tātad ir dots,
ka šis ir 45 grādu leņķis.

00:00:40.210 --> 00:00:42.630


00:00:42.630 --> 00:00:45.530
Pārzīmēšu šo trijstūri mazliet lielāku.

00:00:45.530 --> 00:00:47.530
Trijstūris izskatās šādi.

00:00:47.530 --> 00:00:49.210
Šis ir 45 grādu leņķis,

00:00:49.210 --> 00:00:50.900
tas ir 45 grādu leņķis,

00:00:50.900 --> 00:00:53.790
un šeit ir 90 grādi.

00:00:53.790 --> 00:00:57.330
Nu varam vajadzīgo aprēķināt
45, 45 un 90 grādu trijstūrī.

00:00:57.330 --> 00:00:59.040
Hipotenūza ir 1 vienību gara.

00:00:59.040 --> 00:01:00.380
Šī mala ir x. Šī mala ir x.

00:01:00.380 --> 00:01:00.640


00:01:00.640 --> 00:01:04.430
Abas malas ir vienāda garuma,
jo šis ir vienādsānu trijstūris.

00:01:04.430 --> 00:01:04.920


00:01:04.920 --> 00:01:06.960
Leņķi pie pamata ir vienādi.

00:01:06.960 --> 00:01:10.690
Tātad x kvadrātā plus x kvadrātā

00:01:10.690 --> 00:01:12.960
ir vienāds ar 1 kvadrātā, kas ir 1.

00:01:12.960 --> 00:01:15.200
2 x kvadrātā ir vienāds ar 1;

00:01:15.200 --> 00:01:17.440
x kvadrātā ir vienāds ar 1/2.

00:01:17.440 --> 00:01:20.840
X ir vienāds ar kvadrāsakni no 1/2,

00:01:20.840 --> 00:01:22.780
un tas ir 1 dalīts ar kvadrātsakni no 2.

00:01:22.780 --> 00:01:24.500
Varam to izteikt racionālā formā,

00:01:24.500 --> 00:01:27.330
skaitītāju un saucēju pareizinot
ar kvadrātsakni no 2
dalīts ar kvadrātsakni no 2.

00:01:31.230 --> 00:01:34.950
Iegūstam, ka x ir vienāds
ar kvadrātsakni no 2 dalīts ar 2.

00:01:34.950 --> 00:01:38.770
Tātad šis augstums ir
kvadrātsakne no 2 dalīts ar 2.

00:01:38.770 --> 00:01:41.460
Un tikpat garš būs arī šis attālums.

00:01:41.460 --> 00:01:41.710


00:01:41.710 --> 00:01:43.200
Taču mums vajag tikai augstumu,

00:01:43.200 --> 00:01:46.600
jo sinusa vērtība, šī leņķa sinuss,

00:01:46.600 --> 00:01:47.920
atbilst šim augstumam – y koordinātai.

00:01:47.920 --> 00:01:49.180


00:01:49.180 --> 00:01:52.960
Un mēs noskaidrojām,
ka tas ir kvadrātsakne no 2 dalīts ar 2.

00:01:52.960 --> 00:01:53.890
Šis viss ir atkārtojums –

00:01:53.890 --> 00:02:00.210
mēs to apguvām vienības riņķa video.

00:02:00.210 --> 00:02:04.020
Bet ja nu kādu citu dienu
pienāktu tev klāt un pajautātu:

00:02:04.020 --> 00:02:06.740
"Saki, lūdzu, –

00:02:06.740 --> 00:02:14.930
saki, lūdzu, cik ir arksinuss
no kvadrātsaknes no 2 dalīts ar 2?"

00:02:14.930 --> 00:02:16.190
Kas ir arksinuss?

00:02:16.190 --> 00:02:18.710
Tu, iespējams, apjuktu –
tu zini, kas ir leņķa sinuss,

00:02:18.710 --> 00:02:18.970


00:02:18.970 --> 00:02:24.480
bet te Salmans runā par kaut kādu
jaunu trigonometrisko funkciju.

00:02:24.480 --> 00:02:28.220
Taču patiesībā vienīgais, kas jāzina,
ja vārda sākumā ir šī "ark" daļa...

00:02:28.220 --> 00:02:30.560
to reizēm dēvē arī par INVERSO
JEB APGRIEZTO SINUSU.

00:02:30.560 --> 00:02:30.810


00:02:30.810 --> 00:02:33.590
To varētu pierakstīt arī šādi:

00:02:33.590 --> 00:02:38.420
kāds ir INVERSAIS sinuss
no kvadrātsaknes no 2 dalīts ar 2?

00:02:38.420 --> 00:02:42.900
Būtībā tiek jautāts,
kādam leņķim jānosaka sinuss,

00:02:42.900 --> 00:02:48.310
lai iegūtā vērtība būtu
kvadrātsakne no 2 dalīts ar 2.

00:02:48.310 --> 00:02:52.000
Tātad tiek jautāts,
kādam leņķim jānosaka sinuss,

00:02:52.000 --> 00:02:54.610
lai iegūtu kvadrātsakni no 2 dalīts ar 2.

00:02:54.610 --> 00:03:00.220


00:03:00.220 --> 00:03:02.260


00:03:02.260 --> 00:03:06.890


00:03:06.890 --> 00:03:11.200


00:03:11.200 --> 00:03:14.910


00:03:14.910 --> 00:03:15.820


00:03:15.820 --> 00:03:18.400


00:03:18.400 --> 00:03:21.950


00:03:21.950 --> 00:03:24.080


00:03:24.080 --> 00:03:28.560


00:03:28.560 --> 00:03:30.630


00:03:30.630 --> 00:03:35.760


00:03:35.760 --> 00:03:42.400


00:03:42.400 --> 00:03:51.940


00:03:51.940 --> 00:03:56.120


00:03:56.120 --> 00:03:58.630


00:03:58.630 --> 00:04:01.490


00:04:01.490 --> 00:04:03.030


00:04:03.030 --> 00:04:03.950


00:04:03.950 --> 00:04:05.120


00:04:05.120 --> 00:04:06.960


00:04:06.960 --> 00:04:08.540


00:04:08.540 --> 00:04:11.560


00:04:11.560 --> 00:04:13.130


00:04:13.130 --> 00:04:15.330


00:04:15.330 --> 00:04:18.870


00:04:18.870 --> 00:04:19.960


00:04:19.960 --> 00:04:23.350


00:04:23.350 --> 00:04:25.290


00:04:25.290 --> 00:04:27.700


00:04:27.700 --> 00:04:29.720


00:04:29.720 --> 00:04:31.740


00:04:31.740 --> 00:04:33.540


00:04:33.540 --> 00:04:34.370


00:04:34.370 --> 00:04:37.070


00:04:37.070 --> 00:04:40.340


00:04:40.340 --> 00:04:42.230


00:04:42.230 --> 00:04:47.490


00:04:47.490 --> 00:04:52.280


00:04:52.280 --> 00:04:55.320


00:04:55.320 --> 00:04:58.450


00:04:58.450 --> 00:05:00.340


00:05:00.340 --> 00:05:02.660


00:05:02.660 --> 00:05:04.710


00:05:04.710 --> 00:05:06.990


00:05:06.990 --> 00:05:08.910


00:05:08.910 --> 00:05:10.120


00:05:10.120 --> 00:05:13.160


00:05:13.160 --> 00:05:18.320


00:05:18.320 --> 00:05:21.900


00:05:21.900 --> 00:05:24.502


00:05:24.502 --> 00:05:27.310


00:05:27.310 --> 00:05:30.770


00:05:30.770 --> 00:05:33.840


00:05:33.840 --> 00:05:37.680


00:05:37.680 --> 00:05:39.310


00:05:39.310 --> 00:05:41.570


00:05:41.570 --> 00:05:43.930


00:05:43.930 --> 00:05:45.180


00:05:45.180 --> 00:05:46.360


00:05:46.360 --> 00:05:47.790


00:05:47.790 --> 00:05:50.700


00:05:50.700 --> 00:05:52.630


00:05:52.630 --> 00:05:57.210


00:05:57.210 --> 00:05:58.750


00:05:58.750 --> 00:06:03.840


00:06:03.840 --> 00:06:11.180


00:06:11.180 --> 00:06:14.150


00:06:14.150 --> 00:06:17.110


00:06:17.110 --> 00:06:20.280


00:06:20.280 --> 00:06:21.430


00:06:21.430 --> 00:06:30.450


00:06:30.450 --> 00:06:32.390


00:06:36.480 --> 00:06:37.690


00:06:37.690 --> 00:06:40.100


00:06:40.100 --> 00:06:41.420


00:06:41.420 --> 00:06:42.220


00:06:42.220 --> 00:06:44.730


00:06:44.730 --> 00:06:46.990


00:06:46.990 --> 00:06:48.480


00:06:48.480 --> 00:06:53.550


00:06:53.550 --> 00:06:54.810


00:06:54.810 --> 00:06:56.890


00:06:56.890 --> 00:06:59.690


00:06:59.690 --> 00:07:01.300


00:07:01.300 --> 00:07:04.360


00:07:04.360 --> 00:07:07.760


00:07:07.760 --> 00:07:09.320


00:07:09.320 --> 00:07:15.020


00:07:15.020 --> 00:07:18.800


00:07:18.800 --> 00:07:20.440


00:07:20.440 --> 00:07:24.160


00:07:24.160 --> 00:07:26.090


00:07:26.090 --> 00:07:31.600


00:07:31.600 --> 00:07:33.460


00:07:33.460 --> 00:07:36.110


00:07:36.110 --> 00:07:39.130


00:07:39.130 --> 00:07:44.240


00:07:44.240 --> 00:07:45.520


00:07:45.520 --> 00:07:48.040


00:07:48.040 --> 00:07:52.740


00:07:52.740 --> 00:07:55.680


00:07:55.680 --> 00:07:56.230


00:07:56.230 --> 00:07:57.950


00:07:57.950 --> 00:07:58.530


00:07:58.530 --> 00:08:00.660


00:08:00.660 --> 00:08:03.120


00:08:03.120 --> 00:08:03.890


00:08:03.890 --> 00:08:06.020


00:08:06.020 --> 00:08:07.560


00:08:07.560 --> 00:08:08.850


00:08:08.850 --> 00:08:11.960


00:08:11.960 --> 00:08:14.540


00:08:14.540 --> 00:08:16.870


00:08:16.870 --> 00:08:17.980


00:08:17.980 --> 00:08:19.950


00:08:19.950 --> 00:08:21.250


00:08:21.250 --> 00:08:22.880


00:08:22.880 --> 00:08:24.630


00:08:24.630 --> 00:08:27.415


00:08:27.415 --> 00:08:30.500


00:08:30.500 --> 00:08:32.610


00:08:32.610 --> 00:08:35.140


00:08:35.140 --> 00:08:36.100


00:08:36.100 --> 00:08:37.325


00:08:37.325 --> 00:08:39.970


00:08:39.970 --> 00:08:43.180


00:08:43.180 --> 00:08:44.630


00:08:44.630 --> 00:08:45.210


00:08:45.210 --> 00:08:52.350


00:08:52.350 --> 00:08:54.540


00:08:54.540 --> 00:08:56.070


00:08:56.070 --> 00:08:59.500


00:08:59.500 --> 00:09:04.090


00:09:04.090 --> 00:09:10.630


00:09:10.630 --> 00:09:16.780


00:09:16.780 --> 00:09:19.980


00:09:19.980 --> 00:09:24.680


00:09:24.680 --> 00:09:30.840


00:09:30.840 --> 00:09:34.290


00:09:34.290 --> 00:09:35.310


00:09:35.310 --> 00:09:38.200


00:09:38.200 --> 00:09:39.370


00:09:39.370 --> 00:09:41.060


00:09:41.060 --> 00:09:43.040


00:09:43.040 --> 00:09:45.490


00:09:45.490 --> 00:09:47.840


00:09:47.840 --> 00:09:51.610


00:09:51.610 --> 00:09:59.790


00:09:59.790 --> 00:10:03.800


00:10:03.800 --> 00:10:11.040


00:10:11.040 --> 00:10:13.970


00:10:13.970 --> 00:10:16.030


00:10:16.030 --> 00:10:25.180


00:10:25.180 --> 00:10:26.670


00:10:26.670 --> 00:10:28.710


00:10:28.710 --> 00:10:31.240


00:10:31.240 --> 00:10:34.520