Trigonometrik tengsizliklarni yechish
![Trigonometrik
tengsizliklarni yechish](/data/documents/5bc7e961-448e-454e-880c-88ec5e6f3ad0/page_1.png)
![cos x ≥ a
cos x ≤ a
|a| ≤ 1Trigonometrik tengsizliklarni yechishning umumiy hollari
- arccos a + 2 ?????? n ≤ x ≤ arccos a + 2 ?????? n
arccos a + 2 ?????? n ≤ x ≤ 2 ?????? - arccos a + 2 ?????? n](/data/documents/5bc7e961-448e-454e-880c-88ec5e6f3ad0/page_2.png)
![Xususiy hollarda
cos x ≥ 0
cos x ≤ 0
- /2 + ?????? 2 ?????? n ≤ x ≤ /2 ?????? + 2 ?????? n
?????? /2 + 2 ?????? n ≤ x ≤ 3 /2
?????? + 2 ?????? n](/data/documents/5bc7e961-448e-454e-880c-88ec5e6f3ad0/page_3.png)
![Xususiy hollarda ( а = -1 uchun )
1) cos x ≥ 1
2) cos x > 1
1) X = 2?????? n
2) yechimi yo'q 1) cos x ≤ 1
2 ) cos x < 1
1) X € R
2) X € R , кроме 2
?????? n](/data/documents/5bc7e961-448e-454e-880c-88ec5e6f3ad0/page_4.png)
![Xususiy hollarda :
a > 1 (a < - 1)
cos x ≥ a cos x ≤ a
Yechimi yo’q
(Х € R ) Х € R
(yechimi yo’q )](/data/documents/5bc7e961-448e-454e-880c-88ec5e6f3ad0/page_5.png)
![Trigonometrik tengsizliklarni yechishning umumiy
ko’rinishi
sin x ≥ a sin x ≤ a
arcsin a + 2 ?????? n ≤ x ≤ ?????? – arcsin a + 2 ?????? n
– ?????? arcsin a + 2 ?????? n ≤ x ≤ 2 ?????? + arcsin a + 2 ?????? n|a| ≤ 1](/data/documents/5bc7e961-448e-454e-880c-88ec5e6f3ad0/page_6.png)
![Xususiy hollarda
sin x ≥ 0 sin x ≤ 0
2 ?????? n ≤ x ≤ ?????? + 2 ?????? n
?????? + 2 ?????? n ≤ x ≤ 2 ?????? + 2 ?????? n](/data/documents/5bc7e961-448e-454e-880c-88ec5e6f3ad0/page_7.png)
![Xususiy hollarda ( а = -1 uchun )
1) sin x ≥ 1 1) sin x ≤ 1
2) sin x > 1 2 ) sin x < 1
1) X = /2 + 2?????? ?????? n
2) Yechimi yo’q 1) X € R
2) X € R , /2 + 2
?????? ?????? n(undan
tashqari)](/data/documents/5bc7e961-448e-454e-880c-88ec5e6f3ad0/page_8.png)
![Xususiy hollarda :
a > 1 (a < - 1)
sin x ≥ a sin x ≤ a
yechimi yo'q
(Х € R ) Х € R
(yechimi yo'q )](/data/documents/5bc7e961-448e-454e-880c-88ec5e6f3ad0/page_9.png)
![Trigonometrik tengsizliklarni yechishning umumiy hollari
tg x ≥ a tg x ≤ a
arctg a + ?????? n ≤ x < /2 + ?????? ?????? n
- /2
?????? + ?????? n < x ≤ arctg a + ?????? n](/data/documents/5bc7e961-448e-454e-880c-88ec5e6f3ad0/page_10.png)
![Trigonometrik tengsizliklarni yechishning umumiy hollari
ctg x ≥ a ctg x ≤ a
n < x ≤ arcctg a + n
arcctg a + ?????? n ≤ x < +?????? ?????? n](/data/documents/5bc7e961-448e-454e-880c-88ec5e6f3ad0/page_11.png)
Trigonometrik tengsizliklarni yechish
cos x ≥ a cos x ≤ a |a| ≤ 1Trigonometrik tengsizliklarni yechishning umumiy hollari - arccos a + 2 ?????? n ≤ x ≤ arccos a + 2 ?????? n arccos a + 2 ?????? n ≤ x ≤ 2 ?????? - arccos a + 2 ?????? n
Xususiy hollarda cos x ≥ 0 cos x ≤ 0 - /2 + ?????? 2 ?????? n ≤ x ≤ /2 ?????? + 2 ?????? n ?????? /2 + 2 ?????? n ≤ x ≤ 3 /2 ?????? + 2 ?????? n
Xususiy hollarda ( а = -1 uchun ) 1) cos x ≥ 1 2) cos x > 1 1) X = 2?????? n 2) yechimi yo'q 1) cos x ≤ 1 2 ) cos x < 1 1) X € R 2) X € R , кроме 2 ?????? n
Xususiy hollarda : a > 1 (a < - 1) cos x ≥ a cos x ≤ a Yechimi yo’q (Х € R ) Х € R (yechimi yo’q )