Burchakning radian o’lchovi. Burchakni burish
![Burchakning radian
o’lchovi. Burchakni burish](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_1.png)
![Burchak – ikki nurning bir nuqtadan
chiquvchiα](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_2.png)
![Burchakni o’lchash
•0
60 ](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_3.png)
![Burchakning o’lchov birliklari :
1 minut ( 1 ’) gradusning - qismi
1 Sekund ( 1 ’’) minutning -](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_4.png)
![Bobilliklar quyosh har bir kun uchun bir "qadam"
olishiga ishonishgan, shuning uchun ular aylanani
360 ta teng qismga bo'lishdi, ularning har biri
daraja deb ataladi (lot. Gradus - qadam).](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_5.png)
![Trigonometriyaning rivojlanishi
XIX-asrda burchaklarni o'lchash
uchun yangi o'lchov - radianni
joriy qilish zaruratini keltirib
chiqardi. .](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_6.png)
![Из м ерение углов
1 radian (lotincha radiusdan - g'ildirakning simi) -
yoyi uzunligi aylana radiusiga teng bo'lgan
markaziy burchak](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_7.png)
![Pi – aylana uzunligining
aylanasining diametriga nisbatini
ifodalovchi matematik konstanta](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_8.png)
![Burchakning o’lchov
birliklari
gradus
radian 180
Radian
=](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_9.png)
![ Radian =180 Gradusning radian bilan
ifodalanishi
1
180
. рад](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_10.png)
![ rad иан =180 Gradus o’lchovidan radian
o’lchoviga o’tkazish
n
180
.рад
n](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_11.png)
![ Radian =180 Misollar :
180
30
30
6
180
30
72 72
180
72
52
180
120 120
180
120
3
2
180](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_12.png)
![misollar :
60
1..
3
рад
90
2. .
2
рад
.
180 135
рад
3.
.
4
3
рад
.
180
60
рад
.
180
90
рад
135](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_13.png)
![Radian o’lchovidan gradus
o’lchoviga o’tkazing :
45
10
36 240
150
330 4
18
5
180
270
2
3
360
2
3
4
6
5
6
11 ](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_14.png)
![ rad иан =180 Radian o’lchovidan gradus
o’lchoviga aylantirish
m
180a](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_15.png)
![Misollar :
.
10 рад
1.
10
180
.
9
рад
2.
9180
.
3
4
рад
3.
3
180 4
18
20
240](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_16.png)
![gradus o’lchovidan radianga
aylantiring
.
245
рад
.
5
рад
.
180
рад
.
310
рад
.
4
рад
1
36
5 , 37
.
43
рад
45
600
135](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_17.png)
![Gradus o’lchovini radianda
ifodalang :.
18
11
рад
.
4
11
рад
.
2
11
рад
.
6
17
рад
.
25
рад
. рад
990
495
110
180
450
510](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_18.png)
![Daraja o'lchovidan radianga
aylantirish :
.
180 радn
n
Radianni gradus o’lchoviga
aylantirish :
180
.
m m
рад
](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_19.png)
![xy
O0
54
0 320 0
497 +
–
Окружность с центром в начале систем ы координат
Oxy
и rad , , иусом равны м единице наз ы вается
еди н и чн ой , –
а ограниченны й ей круг
т ри гон омет ри чески м .Koordinata boshi sifatida
aylananing Ox o'qining musbat
qismi bilan kesishgan nuqtasi
olinadi Soat stelkasi bo’ylab
aylanishi .Soat strelkasiga qarama-
qarshi yo’nalishda Birlik aylana](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_20.png)
![45
-60 135
240 150
Ху
0 °180 ° 30 °60 °90 °
270 ° 45°
- 30 °
- 45 °
- 60 °150 °135 ° 120 °
- 120 °- 135 °- 150 ° xy
OBirlik aylanaga joylashtiring
0 30
60 90
180
330
240 270 330
-30
-45
-120
-150 120
360 -135
-210
-210 405
405
360 °](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_21.png)
![2
3
4
3
6
19 Birlik aylanaga joylashtiring 3
4
3
6
19
2
6
11 6
11
417
4
17
43
4
3
2
2
3
2
3
2
4
4
xу
6
5
6
5
](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_22.png)
![xy
O2
0
2
3
III 0 ° < <
90 °
90 ° < < 180 °
180 ° < <
270 °
2
2
3
2 270 ° < <
360 ° I
II
IVchorak
chorak
chorak chorakBirlik aylana](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_23.png)
![xy
O0
25
9
5
0
220 Burchaklar qaysi chorakda
joylashganligini aniqlang:
= 25 °
=
9
5
= 220 °
3
8
= I
chorak
chorak
IV
III
chorak
3
8
chorak II](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_24.png)
![Mustaqil ish
1 Burchaklarni radian o'lchoviga aylantiring, ular qaysi
chorakda joylashganligini aniqlang:
1) 60
2)
145
3)
240 I-variant II variant
1)
320
2)
105
3)
40
2. Burchaklarni graduso'lchoviga aylantiring, ular qaysi
chorakda joylashganligini aniqlang:
.
5
2
рад
.
3
8
рад
1)
2)
.
4
9
рад
.
6
5
рад
1)
2)](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_25.png)
![Javoblari
1.
1)
2)
3) I variant II variant
1)
2)
3)
2. . .
3
ч I рад
1) 72 I ч.
2) 480 II ч. 1) 405 I ч.
2) 150 II ч.
. .
36
29
ч II рад
. .
3
4
ч III рад
. .
9
16
ч IV rad
. .
12
7
ч II рад
. .
9
2
ч I рад
](/data/documents/cfdaea3a-f151-40d7-933c-f40f307dcf2d/page_26.png)
Burchakning radian o’lchovi. Burchakni burish
Burchak – ikki nurning bir nuqtadan chiquvchiα
Burchakni o’lchash •0 60
Burchakning o’lchov birliklari : 1 minut ( 1 ’) gradusning - qismi 1 Sekund ( 1 ’’) minutning -
Bobilliklar quyosh har bir kun uchun bir "qadam" olishiga ishonishgan, shuning uchun ular aylanani 360 ta teng qismga bo'lishdi, ularning har biri daraja deb ataladi (lot. Gradus - qadam).