WEBVTT 00:00:00.910 --> 00:00:03.770 Vítejte u prezentace o radiánech a stupních. 00:00:03.770 --> 00:00:07.010 Všichni již jistě máte nějaké povědomí 00:00:07.010 --> 00:00:07.950 o konceptu stupňů. 00:00:07.950 --> 00:00:10.310 Myslím, že v našich modelech úhlů se musíte dostat 00:00:10.310 --> 00:00:12.370 přes spoustu problémů. 00:00:12.370 --> 00:00:23.460 Určitě víte, že pravý úhel je 90 stupňů. 00:00:23.460 --> 00:00:28.650 Polovina pravého úhlu potom 45 stupňů. 00:00:28.650 --> 00:00:32.630 Také jistě víte, že v kruhu 00:00:32.630 --> 00:00:36.610 - tohle je nejlepší kruh jaký dovedu nakreslit - 00:00:36.610 --> 00:00:38.760 00:00:38.760 --> 00:00:41.010 kruh má 360 stupňů. 00:00:41.010 --> 00:00:44.750 Dnes vám představím další způsob měření úhlů 00:00:44.750 --> 00:00:47.270 a to sice radiány. 00:00:47.270 --> 00:00:52.160 00:00:52.160 --> 00:00:53.450 Co je to radián? 00:00:53.450 --> 00:00:55.650 Začnu s definicí a myslím, 00:00:55.650 --> 00:00:57.105 že to vám dá malou nápovědu, 00:00:57.105 --> 00:00:59.910 proč se to vlastně jmenuje radián. 00:00:59.910 --> 00:01:01.380 00:01:01.380 --> 00:01:02.850 Použiji nástroj na kružnice a nakreslím hezkou kružnici. 00:01:02.850 --> 00:01:10.060 00:01:10.060 --> 00:01:14.270 Aha, pořád používám nástroj na radiány, totiž, kružnice. 00:01:14.270 --> 00:01:14.530 Ok. 00:01:14.530 --> 00:01:19.430 00:01:19.430 --> 00:01:21.630 Tohle je poloměr délky r. 00:01:21.630 --> 00:01:25.500 Radián je úhel, který je protilehlý oblouku. 00:01:25.500 --> 00:01:30.210 Protilehlost znamená, že když tohle je úhel a tohle 00:01:30.210 --> 00:01:34.520 je oblouk a tento úhel je protilehlý tomuto oblouku a tento oblouk 00:01:34.520 --> 00:01:36.020 je protilehlý tomuto úhlu. 00:01:36.020 --> 00:01:41.050 Takže radián (jeden radián) je úhel, který je protilehlý oblouku, 00:01:41.050 --> 00:01:44.130 o délce poloměru. 00:01:44.130 --> 00:01:46.780 Takže délka tohoto je také r. 00:01:46.780 --> 00:01:50.440 A velikost tohoto úhlu je 1 radián. 00:01:50.440 --> 00:01:51.140 V tomhle je docela nepořádek. 00:01:51.140 --> 00:01:52.490 Nakreslím větší kružnici. 00:01:52.490 --> 00:01:55.010 00:01:55.010 --> 00:01:56.640 Tady jí máme. 00:01:56.640 --> 00:01:57.860 Chci to udělat, protože se divím, 00:01:57.860 --> 00:01:58.780 proč se používají radiány. 00:01:58.780 --> 00:02:00.300 Všichni známe stupně. 00:02:00.300 --> 00:02:02.090 Ale když se na tím zamyslíme, 00:02:02.090 --> 00:02:03.100 skutečně to dává smysl. 00:02:03.100 --> 00:02:05.873 Teď nakreslím přímku. 00:02:05.873 --> 00:02:12.980 00:02:12.980 --> 00:02:18.990 Řekněme, že toho je poloměr s délkou r a tohle je oblouk, 00:02:18.990 --> 00:02:21.460 také s délkou r. 00:02:21.460 --> 00:02:28.210 Potom tenhle úhel, jménem theta, je roven jednomu radiánu. 00:02:28.210 --> 00:02:30.220 Teď dává smysl, proč se tomu říká radián. 00:02:30.220 --> 00:02:32.440 Je to trochu jako poloměr (rádius). 00:02:32.440 --> 00:02:35.100 A teď se zeptám: kolik radiánů 00:02:35.100 --> 00:02:37.420 je v kružnici? 00:02:37.420 --> 00:02:41.300 Jestli je tohle r, jaký je celý obvod 00:02:41.300 --> 00:02:42.050 kružnice? 00:02:42.050 --> 00:02:44.630 00:02:44.630 --> 00:02:46.540 Je to 2 pi r, že ano? 00:02:46.540 --> 00:02:50.050 To víte ze základů geometrie. 00:02:50.050 --> 00:02:55.850 Pokud je radián úhel, který náleží oblouku o délce r, 00:02:55.850 --> 00:03:03.650 potom je úhel, který náleží oblouku o délce 2r úhel 2 pi radiánů. 00:03:03.650 --> 00:03:06.970 Takže úhel je 2 pi radiánů. 00:03:06.970 --> 00:03:12.510 00:03:12.510 --> 00:03:14.820 Pokud jste stále zmatení, podívejte se na to takhle. 00:03:14.820 --> 00:03:20.390 00:03:20.390 --> 00:03:22.650 00:03:22.650 --> 00:03:23.500 00:03:23.500 --> 00:03:26.460 00:03:26.460 --> 00:03:27.110 00:03:27.110 --> 00:03:30.130 00:03:30.130 --> 00:03:32.630 00:03:32.630 --> 00:03:35.580 00:03:35.580 --> 00:03:38.130 00:03:38.130 --> 00:03:41.890 00:03:41.890 --> 00:03:46.980 00:03:46.980 --> 00:03:49.920 00:03:49.920 --> 00:03:54.190 00:03:54.190 --> 00:03:57.340 00:03:57.340 --> 00:03:58.970 00:03:58.970 --> 00:04:00.800 00:04:00.800 --> 00:04:04.360 00:04:04.360 --> 00:04:07.080 00:04:07.080 --> 00:04:07.520 00:04:07.520 --> 00:04:09.620 00:04:09.620 --> 00:04:10.950 00:04:10.950 --> 00:04:19.390 00:04:19.390 --> 00:04:22.570 00:04:22.570 --> 00:04:27.040 00:04:27.040 --> 00:04:29.710 00:04:29.710 --> 00:04:31.080 00:04:31.080 --> 00:04:34.000 00:04:34.000 --> 00:04:38.530 00:04:38.530 --> 00:04:39.970 00:04:39.970 --> 00:04:45.410 00:04:45.410 --> 00:04:48.570 00:04:48.570 --> 00:04:53.260 00:04:53.260 --> 00:05:00.440 00:05:00.440 --> 00:05:05.220 00:05:05.220 --> 00:05:06.980 00:05:06.980 --> 00:05:08.740 00:05:08.740 --> 00:05:12.520 00:05:12.520 --> 00:05:15.810 00:05:15.810 --> 00:05:21.450 00:05:21.450 --> 00:05:26.545 00:05:26.545 --> 00:05:31.550 00:05:31.550 --> 00:05:35.210 00:05:35.210 --> 00:05:36.120 00:05:36.120 --> 00:05:37.810 00:05:37.810 --> 00:05:39.680 00:05:39.680 --> 00:05:42.680 00:05:42.680 --> 00:05:46.250 00:05:46.250 --> 00:05:57.250 00:05:57.250 --> 00:06:00.940 00:06:00.940 --> 00:06:02.495 00:06:02.495 --> 00:06:03.540 00:06:03.540 --> 00:06:09.010 00:06:09.010 --> 00:06:12.440 00:06:12.440 --> 00:06:18.410 00:06:18.410 --> 00:06:32.910 00:06:32.910 --> 00:06:36.850 00:06:36.850 --> 00:06:42.360 00:06:42.360 --> 00:06:45.650 00:06:45.650 --> 00:06:49.600 00:06:49.600 --> 00:06:52.610 00:06:52.610 --> 00:06:55.070 00:06:55.070 --> 00:06:56.590 00:06:56.590 --> 00:06:59.700 00:06:59.700 --> 00:07:01.690 00:07:01.690 --> 00:07:03.030 00:07:03.030 --> 00:07:04.920 00:07:04.920 --> 00:07:06.690 00:07:06.690 --> 00:07:08.400 00:07:08.400 --> 00:07:10.200 00:07:10.200 --> 00:07:12.630 00:07:12.630 --> 00:07:15.400 00:07:15.400 --> 00:07:17.570 00:07:17.570 --> 00:07:21.550 00:07:21.550 --> 00:07:23.840 00:07:23.840 --> 00:07:33.060 00:07:33.060 --> 00:07:33.765 00:07:33.765 --> 00:07:37.480 00:07:37.480 --> 00:07:40.660 00:07:40.660 --> 00:07:45.565 00:07:45.565 --> 00:07:55.720 00:07:55.720 --> 00:07:57.930 00:07:57.930 --> 00:08:02.670 00:08:02.670 --> 00:08:05.120 00:08:05.120 --> 00:08:07.270 00:08:07.270 --> 00:08:12.140 00:08:12.140 --> 00:08:18.840 00:08:18.840 --> 00:08:21.660 00:08:21.660 --> 00:08:23.470 00:08:23.470 --> 00:08:24.490 00:08:24.490 --> 00:08:25.500 00:08:25.500 --> 00:08:33.160 00:08:33.160 --> 00:08:38.510 00:08:38.510 --> 00:08:41.585 00:08:41.585 --> 00:08:47.240 00:08:47.240 --> 00:08:48.830 00:08:48.830 --> 00:08:54.480 00:08:54.480 --> 00:08:55.915 00:08:55.915 --> 00:09:00.950 00:09:00.950 --> 00:09:03.200 00:09:03.200 --> 00:09:10.960 00:09:10.960 --> 00:09:19.150 00:09:19.150 --> 00:09:27.220 00:09:27.220 --> 00:09:31.320 00:09:31.320 --> 00:09:36.160 00:09:36.160 --> 00:09:39.630 00:09:39.630 --> 00:09:42.070 00:09:42.070 --> 00:09:45.880 00:09:45.880 --> 00:09:50.210 00:09:50.210 --> 00:09:52.410 00:09:52.410 --> 00:09:54.671