WEBVTT 00:00:00.340 --> 00:00:03.360 အကယ်ရွေ့များကျွန်တော်သင့်ကို လမ်းမှာတွေ့လို့ 00:00:03.360 --> 00:00:07.450 (အထူကြီးမှားရေးမိတယ်) 00:00:07.450 --> 00:00:11.710 ပိုင်(pi)အစား၄ရဲ့ဆိုင်း(sin) ကဘာလဲလို့မေးရင် 00:00:11.710 --> 00:00:14.950 သင်ကradianသုံးရမယ်လို့ထင်မှာပေါ့ 00:00:14.950 --> 00:00:17.510 သင်အလွတ်မှတ်ထားရင်မှတ်မိမယ် ဒါမှမဟုတ် 00:00:17.510 --> 00:00:19.920 ဒီလိုစက်ဝိုင်းလေးဆွဲလိုက်မှာပေါ့ 00:00:19.920 --> 00:00:21.360 အဝိုင်းဆုံးစက်ဝိုင်းတော့မဟုတ်ဘူး 00:00:21.360 --> 00:00:22.220 ဒါပေမဲ့သင်သဘောပေါက်ပါတယ် 00:00:22.220 --> 00:00:23.080 pi အစား ၄ radians က 00:00:23.080 --> 00:00:25.960 ၄၅ဒီကရီနဲ့ညီမျှပါတယ် 00:00:25.960 --> 00:00:26.960 အချင်းဝက်မျဉ်းကိုဆွဲပြီး 00:00:26.960 --> 00:00:29.760 sin ကစက်ဝိုင်းတစ်ခုရဲ့ 00:00:29.760 --> 00:00:31.840 y-ကိုသြဒီနိတ်(coordinate) ဖြစ်ပါတယ် 00:00:31.840 --> 00:00:35.130 ဆိုတော့သင်ကဒီတန်ဖိုးကိုယူမယ်ဆိုရင် 00:00:35.130 --> 00:00:36.250 သင်ကချက်ခြင်း ok 00:00:36.250 --> 00:00:38.910 ဒါက ၄၅ဒီကရီလို့ပြောလို့ရတာပေါ့ 00:00:38.910 --> 00:00:40.210 ကျွန်တော်ဒီတြိဂံကိုအကြီးချဲ့လိုက်မယ် 00:00:40.210 --> 00:00:42.630 တြိဂံကဒီလိုဆိုရင် 00:00:42.630 --> 00:00:45.530 ဒါက ၄၅ဒီကရီ 00:00:45.530 --> 00:00:47.530 ဒါက ၄၅ဒီကရီ 00:00:47.530 --> 00:00:49.210 ဒါက ၉၀ဒီကရီ 00:00:49.210 --> 00:00:50.900 ဒါဆိုသင်က ၄၅-၄၅-၉၀ တြိဂံကို အဖြေရှာလို့ရပြီ 00:00:50.900 --> 00:00:53.790 ဟိုက်ပိုတန်းနယုစ်(hypotenuse)က ၁ 00:00:53.790 --> 00:00:57.330 ဒါက x 00:00:57.330 --> 00:00:59.040 ဒါက x 00:00:59.040 --> 00:00:59.960 သူတို့နှစ်ခုကတန်ဖိုးတူတော့ isosceles traingle ပေါ့ 00:00:59.960 --> 00:01:00.640 သူတို့နှစ်ခုကတန်ဖိုးတူတော့ isosceles traingle ပေါ့ 00:01:00.640 --> 00:01:01.930 အခြေခံထောင့်ကတူတယ် 00:01:01.930 --> 00:01:04.920 ဒါဆို x နှစ်ထပ်အပေါင်း x နှစ်ထပ်က ၁ နှစ်ထပ် 00:01:04.920 --> 00:01:06.960 ၁ နှစ်ထပ်က ၁ 00:01:06.960 --> 00:01:10.690 2x နှစ်ထပ်က ၁ 00:01:10.690 --> 00:01:12.960 x နှစ်ထပ်က ၁ အစား ၂ 00:01:12.960 --> 00:01:15.200 x က ၁ အစား ၂တို့ရဲ့ နှစ်ထပ်ကိန်းရင်း(square root) 00:01:15.200 --> 00:01:17.440 ဒါက ၁ အစား၂ရဲ့နှစ်ထပ်ကိန်းရင်း(square root) 00:01:17.440 --> 00:01:20.840 ရာရှင်နယ်(rational)နံပတ်ပြောင်းရေးဖို့ 00:01:20.840 --> 00:01:22.780 ၂-square root အစား၂-square rootနဲ့မြှောက်ရင် 00:01:22.780 --> 00:01:25.960 ၂-square root အစား၂ရတာပေါ့ 00:01:25.960 --> 00:01:27.330 ဒါဆိုအမြင့်က ၂-square root အစား၂ 00:01:31.230 --> 00:01:34.950 ဒီအတိုင်အတာပါသိချင်တယ်ဆိုရင် 00:01:34.950 --> 00:01:38.770 အတူတူပဲ 00:01:38.770 --> 00:01:40.400 ဒါပေမဲ့ကျွန်တော်တို့ကအမြင့်ပဲလိုချင်တယ် 00:01:40.400 --> 00:01:41.710 ဘာလို့လဲဆိုတော့ဒီ sin တန်ဖိုးကြောင့် 00:01:41.710 --> 00:01:43.090 ဒီ sin တန်ဖိုးကအမြင့်ရဲ့တန်ဖိုးပဲ 00:01:43.090 --> 00:01:46.600 y-coordinateပေါ့ 00:01:46.600 --> 00:01:47.920 ဒါကိုခုနက၂-square root အစား၂ လို့သိထားတယ် 00:01:47.920 --> 00:01:49.180 ဒါကပြန်လေ့လာတာပါ 00:01:49.180 --> 00:01:52.960 စက်ဝိုင်းဗီဒီရိုတုန်းကသင်ပြီးသား 00:01:52.960 --> 00:01:53.890 ဒါပေမဲ့အကယ်ရွေ့များကျွန်တော်က 00:01:53.890 --> 00:02:00.210 သင့်ကိုနောက်နေ့ကျလို့ 00:02:00.210 --> 00:02:02.290 ၂-square root အစား၂ ရဲ့ arcsin ကဘာလဲလို့မေးရင် 00:02:02.290 --> 00:02:08.850 arcsin ကဘာလဲ 00:02:08.850 --> 00:02:14.820 သင်တုန့်ဆိုင်းသွားမလား 00:02:14.820 --> 00:02:16.190 သင်က ထောင့်တစ်ခုရဲ့sinတော့သိတယ် 00:02:16.190 --> 00:02:16.970 ဒီဟာက ဆဲလ် အသစ်ထွင်ထားတဲ့trigonometry 00:02:16.970 --> 00:02:19.180 သင်သိထားရမှာကအရှေ့မှာarcဆိုတဲ့စကားလုံးပါလာရင် 00:02:19.180 --> 00:02:24.480 တစ်ခါတစ်လေ inverse (ပြောင်းပြန်) sin 00:02:24.480 --> 00:02:27.770 လို့လဲခေါ်တယ် 00:02:27.770 --> 00:02:29.455 သင်ကဒါကို ၂-square root အစား၂ ရဲ့ 00:02:29.455 --> 00:02:30.810 sin ပြောင်းပြန်လို့ရေးလို့ရတယ် 00:02:30.810 --> 00:02:33.960 သူက sinရဲ့ဘယ်ထောင့်ကိုယူရင် 00:02:33.960 --> 00:02:38.420 ၂-square root အစား၂ ရမလဲလို့မေးတာ 00:02:38.420 --> 00:02:42.900 ဒါလည်းသူက sinရဲ့ဘယ်ထောင့်ကိုယူရင် 00:02:42.900 --> 00:02:48.310 ၂-square root အစား၂ ရမလဲလို့မေးတာ 00:02:48.310 --> 00:02:52.000 ကျွန်တော်ကဒီနှစ်ခုကို 00:02:52.000 --> 00:02:54.610 (ပြောပြပရစေ) 00:02:54.610 --> 00:03:00.220 ကျွန်တော်ကဒီနှစ်ခုကို sinရဲ့ဘာက 00:03:00.220 --> 00:03:02.260 ၂-square root အစား၂ ရမလဲလို့ပြောင်းရေးလို့ရတယ် 00:03:02.260 --> 00:03:06.890 ဒီလိုမေးရင်ဖြေရတာ 00:03:06.890 --> 00:03:11.200 ပိုမလွယ်ဘူးလား 00:03:11.200 --> 00:03:14.910 sinရဲ့ဘာက၂-square root အစား၂လဲ 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 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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