Toshloq tumani

3. Mustahkamlash. Test yechiladi.
TESTLAR.

1. 
   Agar sinacosa>0 boTsa, a burchak qaysi chorakka tegishli?
   

A) I yoki II В) I yoki III С) I yoki IV
D) II yoki III E) III yoki IV

2. 
   Agar tgacosa>0 boTsa, a burchak qaysi chorakka tegishli?
   

A) II yoki III B) III yoki IV С) I yoki II
D) I yoki III E) I yoki IV

3. 
   Agar sinacosaO boTsa, a burchak qaysi chorakka tegishli?
   

A) I yoki II В) I yoki III С) I yoki IV
D) II yoki IV E) III yoki IV

4. 
   a=sin540°, Z>=cos640°, c=tg545° va d= ctg405° sonlardan qaysi biri manfiy?
   

A) a B) b С) c D) d E) hech qaysisi manfiy emas.

5. 
   Quyidagi sonlardan qaysi biri manfiy?
   

A) tg247°-sinl25° B) ctg215°-cos300° C) tgl35°-ctg340°
D) sin247°-cos276° E) sin260°-cosl55°

6. 
   Quyidagi sonlardan qaysi biri musbat?
   

ДЧ ctgl%l° cos340° _n sin 148°
’ sin316° ’ sinl85° ’ cos317°
_D) ctg\05° _E) £215°
^ /g-185⁰ ^ cosl25°

7. 
   Quyidagi sonlardan qaysi biri manfiy?
   

A) sinl22°-cos322° B) cosl48°-cos289° C) tgl96°-ctgl89°
D) tg220°-sinl00° E) ctg320°-cosl86°

8. 
   Quyidagi sonlardan qaysi biri manfiy?
   

_D) ctgllO^{0 }} c£324°

E) fg40°-fgl89⁰


9. M


cos 320° _ ctg\ 87°
sin217° ’ ~ £340° ’


lg\85" sin 140°


va Q


sin 135" c&140°


sonli ifodalaming qaysi biri


musbat?


A) M B) N C)R D) Q E) hech qaysisi.
10. Quyidagilardan qaysi biri musbat?
A) cos3 B) sin4 C) sin2 D) tg2 E) cos9

11. 
    5sin90⁰+2cos0⁰-2sin270⁰+10cosl80⁰ ni hisoblang.
    

A) -3 B)-6 C)-l D) 19 E) 9

11. 
    3tg0⁰+2cos90⁰+3sin270°-3cosl80⁰ ni hisoblang.
    

A) 6 B)0 C)-6 D) 9 E) -9

11. 
    sinl80⁰+sin270⁰-ctg90°+ tgl80°-cos90° ni hisoblang.
    

A) -1 B)0 C)1 D) -2 E) 2

11. 
    sinl050°-cos(-90°)+ctg660⁰ ni hisoblang.
    

A) S-\ В) C) -³⁺^ D) 0,5 + л/з E) 2V3

11. 
    sin(-45°)+cos405°+tg(-945⁰) ni hisoblang.
    

A) 1 B)-l C)V2-1 D) -2V2 E) V2+I

11. 
    Quyidagi airmalardan qaysi birining qiymati manfiy ?
    

A) sinl40°-sinl50° B) cosl0°-cos50° C) tg87°-tg85°
D) ctg87°-ctg85° E) cos75°-sinl0°

4. 
   Darsni yakunlash.
   
5. 
   Uyga vazifa: test yechish tematik axborotnomalardan
   

Tayyorladi:
Tekshirdi: OTIBDO‘ :




Sana:


45-mashs‘ulot
Dars mavzusi. Trigonometrik funksiyalarning qo‘shish teoremalari.
Dars maqsadlari: o‘quvchilarga trigonometrik funksiyalarning qo‘shish teoremalari ni o‘rgatish, ulaming fanga qiziqishlarini oshirish.


Darsning borishi:

1. 
   Tashkiliy qism.
   
2. 
   Trigonometrik funksiyalarning qo‘shish teoremalari.
   

Trigonometrik funksiyalarning qo‘shish teoremalari.
Teorema. Ikki argument yig‘indisi (ayirmasi) ning kosinusi argumentlar kosinuslarini ko‘paytmasidan shu argumentlar sinuslari ko‘paytmasini ayirilganiga (qo‘shilganiga) teng boMadi:
cos(a±p)= cos a cos P +sin a sin p
Teorema. Ikki argument yig‘indisi (ayirmasi) ning sinusi birinchi argument sinusini ikkinchi argument kosinusiga ko‘paytmasiga birinchi argument kosinusini ikkinchi argument sinusiga ko‘paytmasini qo‘shilganiga (ayrilganiga) teng boTadi:
sin(a ± p) = sin a cos P ± cos a sin p


Teorema. a va P argumentlarning har qanday qiymatida:


tg(a ± P)


tga + rgp 1 + tgatgft


1-misol: sin 75° ni hisoblang.
Yechish:
sin 75° = sin(45° + 30°) = sin 45° • cos 30° + cos 45° - sin 30°


42 V3 ₊V2 J_


2 2 2 2


2-misol:
Yechish:


sm 105° ni hisoblang.


sin 105° = sin(60° + 45°) = sin 60° • cos 45° + cos 60° • sin 45° =
₌ £Л₊1.^. ₌ й.Ш₊1\
2 2 2 2 4 ^{v p}


3-misol: cos 120° = cos(90° + 30°) = cos90°-cos30°-sin90°-sin30°


0.7Y.I
2 2





\_
2’

4. 
   misol:
   

cos 15° = cos(45° - 30°) = cos 45° • cos 30° + sin 45° • sin 30°

4. 
   misol:
   

42 4з_₊4i


2 2 2 2





tg75° = tg(45° + 30°)


tg45° + tg30°
l-tg45°Tg30°


6-misol:


1 +






7з


Уз+i (Уз+i)²
л/3-1 2


3 + 2V3+1
2


tg45°-tg30°
l-tg45°Tg30°

^l~j

₁₊₁.-L


Уз-i (>/3-i) 3-2V3+1
л/з+1


tgl5° = tg(45° - 30°)


2


2

3. Mustahkamlash. Test yechiladi.

TESTLAR.

1. 
   Agar a=-45° va P=15° boTsa, cos(a+P)+2sinasinP ning qiymatini toping.
   

A)-I B)^ C)-


VI


D) — 2


E) i 2


3 5 л
2. Agar sina = -,sinp =—, -<a va - < p < л boTsa, sin(a-P) ning qiymati qanchaga


teng boTadi ?
A)-


16
65


B) — 65


C) —
65
-0


D)-


56
65


E) - — 13


3. Agar tg(a-P)=5 va a=45 boTsa, tgP ning qiymati hisoblang.


A) — 3


в) -V