1
00:00:00,340 --> 00:00:03,360
အကယ်ရွေ့များကျွန်တော်သင့်ကို
လမ်းမှာတွေ့လို့

2
00:00:03,360 --> 00:00:07,450
(အထူကြီးမှားရေးမိတယ်)

3
00:00:07,450 --> 00:00:11,710
ပိုင်(pi)အစား၄ရဲ့ဆိုင်း(sin)
ကဘာလဲလို့မေးရင်

4
00:00:11,710 --> 00:00:14,950
သင်ကradianသုံးရမယ်လို့ထင်မှာပေါ့

5
00:00:14,950 --> 00:00:17,510
သင်အလွတ်မှတ်ထားရင်မှတ်မိမယ်
ဒါမှမဟုတ်

6
00:00:17,510 --> 00:00:19,920
ဒီလိုစက်ဝိုင်းလေးဆွဲလိုက်မှာပေါ့

7
00:00:19,920 --> 00:00:21,360
အဝိုင်းဆုံးစက်ဝိုင်းတော့မဟုတ်ဘူး

8
00:00:21,360 --> 00:00:22,220
ဒါပေမဲ့သင်သဘောပေါက်ပါတယ်

9
00:00:22,220 --> 00:00:23,080
pi အစား ၄ radians က

10
00:00:23,080 --> 00:00:25,960
၄၅ဒီကရီနဲ့ညီမျှပါတယ်

11
00:00:25,960 --> 00:00:26,960
အချင်းဝက်မျဉ်းကိုဆွဲပြီး

12
00:00:26,960 --> 00:00:29,760
sin ကစက်ဝိုင်းတစ်ခုရဲ့

13
00:00:29,760 --> 00:00:31,840
y-ကိုသြဒီနိတ်(coordinate) ဖြစ်ပါတယ်

14
00:00:31,840 --> 00:00:35,130
ဆိုတော့သင်ကဒီတန်ဖိုးကိုယူမယ်ဆိုရင်

15
00:00:35,130 --> 00:00:36,250
သင်ကချက်ခြင်း ok

16
00:00:36,250 --> 00:00:38,910
ဒါက ၄၅ဒီကရီလို့ပြောလို့ရတာပေါ့

17
00:00:38,910 --> 00:00:40,210
ကျွန်တော်ဒီတြိဂံကိုအကြီးချဲ့လိုက်မယ်

18
00:00:40,210 --> 00:00:42,630
တြိဂံကဒီလိုဆိုရင်

19
00:00:42,630 --> 00:00:45,530
ဒါက ၄၅ဒီကရီ

20
00:00:45,530 --> 00:00:47,530
ဒါက ၄၅ဒီကရီ

21
00:00:47,530 --> 00:00:49,210
ဒါက ၉၀ဒီကရီ

22
00:00:49,210 --> 00:00:50,900
ဒါဆိုသင်က ၄၅-၄၅-၉၀ တြိဂံကို
အဖြေရှာလို့ရပြီ

23
00:00:50,900 --> 00:00:53,790
ဟိုက်ပိုတန်းနယုစ်(hypotenuse)က ၁

24
00:00:53,790 --> 00:00:57,330
ဒါက x

25
00:00:57,330 --> 00:00:59,040
ဒါက x

26
00:00:59,040 --> 00:00:59,960
သူတို့နှစ်ခုကတန်ဖိုးတူတော့ 
isosceles traingle ပေါ့

27
00:00:59,960 --> 00:01:00,640
သူတို့နှစ်ခုကတန်ဖိုးတူတော့ 
isosceles traingle ပေါ့

28
00:01:00,640 --> 00:01:01,930
အခြေခံထောင့်ကတူတယ်

29
00:01:01,930 --> 00:01:04,920
ဒါဆို x နှစ်ထပ်အပေါင်း x နှစ်ထပ်က ၁ နှစ်ထပ်

30
00:01:04,920 --> 00:01:06,960
၁ နှစ်ထပ်က ၁

31
00:01:06,960 --> 00:01:10,690
2x နှစ်ထပ်က ၁

32
00:01:10,690 --> 00:01:12,960
x နှစ်ထပ်က ၁ အစား ၂

33
00:01:12,960 --> 00:01:15,200
x က ၁ အစား ၂တို့ရဲ့
နှစ်ထပ်ကိန်းရင်း(square root)

34
00:01:15,200 --> 00:01:17,440
ဒါက ၁ အစား၂ရဲ့နှစ်ထပ်ကိန်းရင်း(square root)

35
00:01:17,440 --> 00:01:20,840
ရာရှင်နယ်(rational)နံပတ်ပြောင်းရေးဖို့

36
00:01:20,840 --> 00:01:22,780
၂-square root အစား၂-square rootနဲ့မြှောက်ရင်

37
00:01:22,780 --> 00:01:25,960
၂-square root အစား၂ရတာပေါ့

38
00:01:25,960 --> 00:01:27,330
ဒါဆိုအမြင့်က ၂-square root အစား၂

39
00:01:31,230 --> 00:01:34,950
ဒီအတိုင်အတာပါသိချင်တယ်ဆိုရင်

40
00:01:34,950 --> 00:01:38,770
အတူတူပဲ

41
00:01:38,770 --> 00:01:40,400
ဒါပေမဲ့ကျွန်တော်တို့ကအမြင့်ပဲလိုချင်တယ်

42
00:01:40,400 --> 00:01:41,710
ဘာလို့လဲဆိုတော့ဒီ sin တန်ဖိုးကြောင့်

43
00:01:41,710 --> 00:01:43,090
ဒီ sin တန်ဖိုးကအမြင့်ရဲ့တန်ဖိုးပဲ

44
00:01:43,090 --> 00:01:46,600
y-coordinateပေါ့

45
00:01:46,600 --> 00:01:47,920
ဒါကိုခုနက၂-square root အစား၂
လို့သိထားတယ်

46
00:01:47,920 --> 00:01:49,180
ဒါကပြန်လေ့လာတာပါ

47
00:01:49,180 --> 00:01:52,960
စက်ဝိုင်းဗီဒီရိုတုန်းကသင်ပြီးသား

48
00:01:52,960 --> 00:01:53,890
ဒါပေမဲ့အကယ်ရွေ့များကျွန်တော်က

49
00:01:53,890 --> 00:02:00,210
သင့်ကိုနောက်နေ့ကျလို့

50
00:02:00,210 --> 00:02:02,290
၂-square root အစား၂ ရဲ့ arcsin ကဘာလဲလို့မေးရင်

51
00:02:02,290 --> 00:02:08,850
arcsin ကဘာလဲ

52
00:02:08,850 --> 00:02:14,820
သင်တုန့်ဆိုင်းသွားမလား

53
00:02:14,820 --> 00:02:16,190
သင်က ထောင့်တစ်ခုရဲ့sinတော့သိတယ်

54
00:02:16,190 --> 00:02:16,970
ဒီဟာက ဆဲလ် အသစ်ထွင်ထားတဲ့trigonometry

55
00:02:16,970 --> 00:02:19,180
သင်သိထားရမှာကအရှေ့မှာarcဆိုတဲ့စကားလုံးပါလာရင်

56
00:02:19,180 --> 00:02:24,480
တစ်ခါတစ်လေ inverse (ပြောင်းပြန်) sin

57
00:02:24,480 --> 00:02:27,770
လို့လဲခေါ်တယ်

58
00:02:27,770 --> 00:02:29,455
သင်ကဒါကို ၂-square root အစား၂ ရဲ့

59
00:02:29,455 --> 00:02:30,810
sin ပြောင်းပြန်လို့ရေးလို့ရတယ်

60
00:02:30,810 --> 00:02:33,960
သူက sinရဲ့ဘယ်ထောင့်ကိုယူရင်

61
00:02:33,960 --> 00:02:38,420
၂-square root အစား၂ ရမလဲလို့မေးတာ

62
00:02:38,420 --> 00:02:42,900
ဒါလည်းသူက sinရဲ့ဘယ်ထောင့်ကိုယူရင်

63
00:02:42,900 --> 00:02:48,310
၂-square root အစား၂ ရမလဲလို့မေးတာ

64
00:02:48,310 --> 00:02:52,000
ကျွန်တော်ကဒီနှစ်ခုကို

65
00:02:52,000 --> 00:02:54,610
(ပြောပြပရစေ)

66
00:02:54,610 --> 00:03:00,220
ကျွန်တော်ကဒီနှစ်ခုကို sinရဲ့ဘာက

67
00:03:00,220 --> 00:03:02,260
၂-square root အစား၂ ရမလဲလို့ပြောင်းရေးလို့ရတယ်

68
00:03:02,260 --> 00:03:06,890
ဒီလိုမေးရင်ဖြေရတာ

69
00:03:06,890 --> 00:03:11,200
ပိုမလွယ်ဘူးလား

70
00:03:11,200 --> 00:03:14,910
sinရဲ့ဘာက၂-square root အစား၂လဲ

71
00:03:14,910 --> 00:03:15,820


72
00:03:15,820 --> 00:03:18,400


73
00:03:18,400 --> 00:03:21,950


74
00:03:21,950 --> 00:03:24,080


75
00:03:24,080 --> 00:03:28,560


76
00:03:28,560 --> 00:03:30,630


77
00:03:30,630 --> 00:03:35,760


78
00:03:35,760 --> 00:03:42,400


79
00:03:42,400 --> 00:03:51,940


80
00:03:51,940 --> 00:03:56,120


81
00:03:56,120 --> 00:03:58,630


82
00:03:58,630 --> 00:04:01,490


83
00:04:01,490 --> 00:04:03,030


84
00:04:03,030 --> 00:04:03,950


85
00:04:03,950 --> 00:04:05,120


86
00:04:05,120 --> 00:04:06,960


87
00:04:06,960 --> 00:04:08,540


88
00:04:08,540 --> 00:04:11,560


89
00:04:11,560 --> 00:04:13,130


90
00:04:13,130 --> 00:04:15,330


91
00:04:15,330 --> 00:04:18,870


92
00:04:18,870 --> 00:04:19,960


93
00:04:19,960 --> 00:04:23,350


94
00:04:23,350 --> 00:04:25,290


95
00:04:25,290 --> 00:04:27,700


96
00:04:27,700 --> 00:04:29,720


97
00:04:29,720 --> 00:04:31,740


98
00:04:31,740 --> 00:04:33,540


99
00:04:33,540 --> 00:04:34,370


100
00:04:34,370 --> 00:04:37,070


101
00:04:37,070 --> 00:04:40,340


102
00:04:40,340 --> 00:04:42,230


103
00:04:42,230 --> 00:04:47,490


104
00:04:47,490 --> 00:04:52,280


105
00:04:52,280 --> 00:04:55,320


106
00:04:55,320 --> 00:04:58,450


107
00:04:58,450 --> 00:05:00,340


108
00:05:00,340 --> 00:05:02,660


109
00:05:02,660 --> 00:05:04,710


110
00:05:04,710 --> 00:05:06,990


111
00:05:06,990 --> 00:05:08,910


112
00:05:08,910 --> 00:05:10,120


113
00:05:10,120 --> 00:05:13,160


114
00:05:13,160 --> 00:05:18,320


115
00:05:18,320 --> 00:05:21,900


116
00:05:21,900 --> 00:05:24,502


117
00:05:24,502 --> 00:05:27,310


118
00:05:27,310 --> 00:05:30,770


119
00:05:30,770 --> 00:05:33,840


120
00:05:33,840 --> 00:05:37,680


121
00:05:37,680 --> 00:05:39,310


122
00:05:39,310 --> 00:05:41,570


123
00:05:41,570 --> 00:05:43,930


124
00:05:43,930 --> 00:05:45,180


125
00:05:45,180 --> 00:05:46,360


126
00:05:46,360 --> 00:05:47,790


127
00:05:47,790 --> 00:05:50,700


128
00:05:50,700 --> 00:05:52,630


129
00:05:52,630 --> 00:05:57,210


130
00:05:57,210 --> 00:05:58,750


131
00:05:58,750 --> 00:06:03,840


132
00:06:03,840 --> 00:06:11,180


133
00:06:11,180 --> 00:06:14,150


134
00:06:14,150 --> 00:06:17,110


135
00:06:17,110 --> 00:06:20,280


136
00:06:20,280 --> 00:06:21,430


137
00:06:21,430 --> 00:06:30,450


138
00:06:30,450 --> 00:06:32,390


139
00:06:36,480 --> 00:06:37,690


140
00:06:37,690 --> 00:06:40,100


141
00:06:40,100 --> 00:06:41,420


142
00:06:41,420 --> 00:06:42,220


143
00:06:42,220 --> 00:06:44,730


144
00:06:44,730 --> 00:06:46,990


145
00:06:46,990 --> 00:06:48,480


146
00:06:48,480 --> 00:06:53,550


147
00:06:53,550 --> 00:06:54,810


148
00:06:54,810 --> 00:06:56,890


149
00:06:56,890 --> 00:06:59,690


150
00:06:59,690 --> 00:07:01,300


151
00:07:01,300 --> 00:07:04,360


152
00:07:04,360 --> 00:07:07,760


153
00:07:07,760 --> 00:07:09,320


154
00:07:09,320 --> 00:07:15,020


155
00:07:15,020 --> 00:07:18,800


156
00:07:18,800 --> 00:07:20,440


157
00:07:20,440 --> 00:07:24,160


158
00:07:24,160 --> 00:07:26,090


159
00:07:26,090 --> 00:07:31,600


160
00:07:31,600 --> 00:07:33,460


161
00:07:33,460 --> 00:07:36,110


162
00:07:36,110 --> 00:07:39,130


163
00:07:39,130 --> 00:07:44,240


164
00:07:44,240 --> 00:07:45,520


165
00:07:45,520 --> 00:07:48,040


166
00:07:48,040 --> 00:07:52,740


167
00:07:52,740 --> 00:07:55,680


168
00:07:55,680 --> 00:07:56,230


169
00:07:56,230 --> 00:07:57,950


170
00:07:57,950 --> 00:07:58,530


171
00:07:58,530 --> 00:08:00,660


172
00:08:00,660 --> 00:08:03,120


173
00:08:03,120 --> 00:08:03,890


174
00:08:03,890 --> 00:08:06,020


175
00:08:06,020 --> 00:08:07,560


176
00:08:07,560 --> 00:08:08,850


177
00:08:08,850 --> 00:08:11,960


178
00:08:11,960 --> 00:08:14,540


179
00:08:14,540 --> 00:08:16,870


180
00:08:16,870 --> 00:08:17,980


181
00:08:17,980 --> 00:08:19,950


182
00:08:19,950 --> 00:08:21,250


183
00:08:21,250 --> 00:08:22,880


184
00:08:22,880 --> 00:08:24,630


185
00:08:24,630 --> 00:08:27,415


186
00:08:27,415 --> 00:08:30,500


187
00:08:30,500 --> 00:08:32,610


188
00:08:32,610 --> 00:08:35,140


189
00:08:35,140 --> 00:08:36,100


190
00:08:36,100 --> 00:08:37,325


191
00:08:37,325 --> 00:08:39,970


192
00:08:39,970 --> 00:08:43,180


193
00:08:43,180 --> 00:08:44,630


194
00:08:44,630 --> 00:08:45,210


195
00:08:45,210 --> 00:08:52,350


196
00:08:52,350 --> 00:08:54,540


197
00:08:54,540 --> 00:08:56,070


198
00:08:56,070 --> 00:08:59,500


199
00:08:59,500 --> 00:09:04,090


200
00:09:04,090 --> 00:09:10,630


201
00:09:10,630 --> 00:09:16,780


202
00:09:16,780 --> 00:09:19,980


203
00:09:19,980 --> 00:09:24,680


204
00:09:24,680 --> 00:09:30,840


205
00:09:30,840 --> 00:09:34,290


206
00:09:34,290 --> 00:09:35,310


207
00:09:35,310 --> 00:09:38,200


208
00:09:38,200 --> 00:09:39,370


209
00:09:39,370 --> 00:09:41,060


210
00:09:41,060 --> 00:09:43,040


211
00:09:43,040 --> 00:09:45,490


212
00:09:45,490 --> 00:09:47,840


213
00:09:47,840 --> 00:09:51,610


214
00:09:51,610 --> 00:09:59,790


215
00:09:59,790 --> 00:10:03,800


216
00:10:03,800 --> 00:10:11,040


217
00:10:11,040 --> 00:10:13,970


218
00:10:13,970 --> 00:10:16,030


219
00:10:16,030 --> 00:10:25,180


220
00:10:25,180 --> 00:10:26,670


221
00:10:26,670 --> 00:10:28,710


222
00:10:28,710 --> 00:10:31,240


223
00:10:31,240 --> 00:10:34,520